{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian Processes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "[Gaussian Processes](https://en.wikipedia.org/wiki/Gaussian_process) have been used in supervised, unsupervised, and even reinforcement learning problems and are described by an elegant mathematical theory (for an overview of the subject see [1, 4]). They are also very attractive conceptually, since they offer an intuitive way to define priors over functions. And finally, since Gaussian Processes are formulated in a Bayesian setting, they come equipped with a powerful notion of uncertainty. \n",
    "\n",
    "Happily, Pyro offers some support for Gaussian Processes in the `pyro.contrib.gp` module. The goal of this tutorial is to give a brief introduction to Gaussian Processes (GPs) in the context of this module. We will mostly be focusing on how to use the GP interface in Pyro and refer the reader to the references for more details about GPs in general.\n",
    "\n",
    "The model we're interested in is defined by\n",
    "$$f \\sim \\mathcal{GP}\\left(0, \\mathbf{K}_f(x, x')\\right)$$\n",
    "\n",
    "and\n",
    "$$y = f(x) + \\epsilon,\\quad \\epsilon \\sim \\mathcal{N}\\left(0, \\beta^{-1}\\mathbf{I}\\right).$$\n",
    "\n",
    "Here $x, x' \\in\\mathbf{X}$ are points in the input space and $y\\in\\mathbf{Y}$ is a point in the output space. $f$ is a draw from the GP prior specified by the kernel $\\mathbf{K}_f$ and represents a function from $\\mathbf{X}$ to $\\mathbf{Y}$. Finally, $\\epsilon$ represents Gaussian observation noise.\n",
    "\n",
    "We will use the [radial basis function kernel](https://en.wikipedia.org/wiki/Radial_basis_function_kernel) (RBF kernel) as the kernel of our GP:\n",
    "$$ k(x,x') = \\sigma^2 \\exp\\left(-\\frac{\\|x-x'\\|^2}{2l^2}\\right).$$\n",
    "\n",
    "Here $\\sigma^2$ and $l$ are parameters that specify the kernel; specifically, $\\sigma^2$ is a variance or amplitude squared and $l$ is a lengthscale. We'll get some intuition for these parameters below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we import necessary modules."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "import pyro\n",
    "import pyro.contrib.gp as gp\n",
    "import pyro.distributions as dist\n",
    "\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "\n",
    "import seaborn as sns\n",
    "from sklearn.metrics import confusion_matrix, ConfusionMatrixDisplay\n",
    "\n",
    "\n",
    "smoke_test = \"CI\" in os.environ  # ignore; used to check code integrity in the Pyro repo\n",
    "assert pyro.__version__.startswith('1.9.1')\n",
    "pyro.set_rng_seed(0)\n",
    "torch.set_default_tensor_type(torch.DoubleTensor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Throughout the tutorial we'll want to visualize GPs. So we define a helper function for plotting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# note that this helper function does three different things:\n",
    "# (i) plots the observed data;\n",
    "# (ii) plots the predictions from the learned GP after conditioning on data;\n",
    "# (iii) plots samples from the GP prior (with no conditioning on observed data)\n",
    "\n",
    "\n",
    "def plot(\n",
    "    plot_observed_data=False,\n",
    "    plot_predictions=False,\n",
    "    n_prior_samples=0,\n",
    "    model=None,\n",
    "    kernel=None,\n",
    "    n_test=500,\n",
    "    ax=None,\n",
    "):\n",
    "\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots(figsize=(12, 6))\n",
    "    if plot_observed_data:\n",
    "        ax.plot(X.numpy(), y.numpy(), \"kx\")\n",
    "    if plot_predictions:\n",
    "        Xtest = torch.linspace(-0.5, 5.5, n_test)  # test inputs\n",
    "        # compute predictive mean and variance\n",
    "        with torch.no_grad():\n",
    "            if type(model) == gp.models.VariationalSparseGP:\n",
    "                mean, cov = model(Xtest, full_cov=True)\n",
    "            else:\n",
    "                mean, cov = model(Xtest, full_cov=True, noiseless=False)\n",
    "        sd = cov.diag().sqrt()  # standard deviation at each input point x\n",
    "        ax.plot(Xtest.numpy(), mean.numpy(), \"r\", lw=2)  # plot the mean\n",
    "        ax.fill_between(\n",
    "            Xtest.numpy(),  # plot the two-sigma uncertainty about the mean\n",
    "            (mean - 2.0 * sd).numpy(),\n",
    "            (mean + 2.0 * sd).numpy(),\n",
    "            color=\"C0\",\n",
    "            alpha=0.3,\n",
    "        )\n",
    "    if n_prior_samples > 0:  # plot samples from the GP prior\n",
    "        Xtest = torch.linspace(-0.5, 5.5, n_test)  # test inputs\n",
    "        noise = (\n",
    "            model.noise\n",
    "            if type(model) != gp.models.VariationalSparseGP\n",
    "            else model.likelihood.variance\n",
    "        )\n",
    "        cov = kernel.forward(Xtest) + noise.expand(n_test).diag()\n",
    "        samples = dist.MultivariateNormal(\n",
    "            torch.zeros(n_test), covariance_matrix=cov\n",
    "        ).sample(sample_shape=(n_prior_samples,))\n",
    "        ax.plot(Xtest.numpy(), samples.numpy().T, lw=2, alpha=0.4)\n",
    "\n",
    "    ax.set_xlim(-0.5, 5.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data\n",
    "\n",
    "The data consist of $20$ points sampled from\n",
    "$$ y = 0.5\\sin(3x) + \\epsilon, \\quad \\epsilon \\sim \\mathcal{N}(0, 0.2).$$\n",
    "\n",
    "with $x$ sampled uniformly from the interval $[0, 5]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 20\n",
    "X = dist.Uniform(0.0, 5.0).sample(sample_shape=(N,))\n",
    "y = 0.5 * torch.sin(3 * X) + dist.Normal(0.0, 0.2).sample(sample_shape=(N,))\n",
    "\n",
    "plot(plot_observed_data=True)  # let's plot the observed data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define model\n",
    "\n",
    "First we define a RBF kernel, specifying the values of the two hyperparameters `variance` and `lengthscale`. Then we construct a `GPRegression` object. Here we feed in another hyperparameter, `noise`, that corresponds to $\\epsilon$ above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "kernel = gp.kernels.RBF(\n",
    "    input_dim=1, variance=torch.tensor(6.0), lengthscale=torch.tensor(0.05)\n",
    ")\n",
    "gpr = gp.models.GPRegression(X, y, kernel, noise=torch.tensor(0.2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see what samples from this GP function prior look like. Note that this is _before_ we've conditioned on the data. The shape these functions take&mdash;their smoothness, their vertical scale, etc.&mdash;is controlled by the GP kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(model=gpr, kernel=kernel, n_prior_samples=2)\n",
    "_ = plt.ylim((-8, 8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, if we keep the same `variance` and `noise` and increase the `lengthscale`, we will see smoother function samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kernel2 = gp.kernels.RBF(\n",
    "    input_dim=1, variance=torch.tensor(6.0), lengthscale=torch.tensor(1)\n",
    ")\n",
    "gpr2 = gp.models.GPRegression(X, y, kernel2, noise=torch.tensor(0.2))\n",
    "plot(model=gpr2, kernel=kernel2, n_prior_samples=2)\n",
    "_ = plt.ylim((-8, 8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, if we make `variance` and `noise` smaller we will see function samples with smaller vertical amplitude."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kernel3 = gp.kernels.RBF(\n",
    "    input_dim=1, variance=torch.tensor(1.0), lengthscale=torch.tensor(1)\n",
    ")\n",
    "gpr3 = gp.models.GPRegression(X, y, kernel3, noise=torch.tensor(0.01))\n",
    "plot(model=gpr3, kernel=kernel3, n_prior_samples=2)\n",
    "_ = plt.ylim((-8, 8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference\n",
    "\n",
    "In the above we set the kernel hyperparameters by hand. If we want to learn the hyperparameters from the data, we need to do inference. In the simplest (conjugate) case we do gradient ascent on the log marginal likelihood. In `pyro.contrib.gp`, we can use any [PyTorch optimizer](https://pytorch.org/docs/stable/optim.html) to optimize parameters of a model. In addition, we need a loss function which takes inputs are the pair model and guide and returns an ELBO loss (see [SVI Part I](svi_part_i.ipynb) tutorial)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = torch.optim.Adam(gpr.parameters(), lr=0.005)\n",
    "loss_fn = pyro.infer.Trace_ELBO().differentiable_loss\n",
    "losses = []\n",
    "variances = []\n",
    "lengthscales = []\n",
    "noises = []\n",
    "num_steps = 2000 if not smoke_test else 2\n",
    "for i in range(num_steps):\n",
    "    variances.append(gpr.kernel.variance.item())\n",
    "    noises.append(gpr.noise.item())\n",
    "    lengthscales.append(gpr.kernel.lengthscale.item())\n",
    "    optimizer.zero_grad()\n",
    "    loss = loss_fn(gpr.model, gpr.guide)\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    losses.append(loss.item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's plot the loss curve after 2000 steps of training\n",
    "def plot_loss(loss):\n",
    "    plt.plot(loss)\n",
    "    plt.xlabel(\"Iterations\")\n",
    "    _ = plt.ylabel(\"Loss\")  # supress output text\n",
    "\n",
    "\n",
    "plot_loss(losses)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if we're learned anything reasonable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(model=gpr, plot_observed_data=True, plot_predictions=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the thick red curve is the mean prediction and the blue band represents the 2-sigma uncertainty around the mean. It seems we learned reasonable kernel hyperparameters, as both the mean and uncertainty give a reasonable fit to the data. (Note that learning could have easily gone wrong if we e.g. chose too large of a learning rate or chose bad initital hyperparameters.)\n",
    "\n",
    "Note that the kernel is only well-defined if `variance` and `lengthscale` are positive. Under the hood Pyro is using PyTorch constraints (see [docs](http://pytorch.org/docs/master/distributions.html#module-torch.distributions.constraints)) to ensure that hyperparameters are constrained to the appropriate domains. Let's see the constrained values we've learned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.21701954305171967"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gpr.kernel.variance.item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.513454258441925"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gpr.kernel.lengthscale.item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04248063638806343"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gpr.noise.item()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The period of the sinusoid that generated the data is $T = 2\\pi/3 \\approx 2.09$ so learning a lengthscale that's approximiately equal to a quarter period makes sense. Let us now try to animate and see how our model improves over the training iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "\n",
    "\n",
    "def update(iteration):\n",
    "    pyro.clear_param_store()\n",
    "    ax.cla()\n",
    "    kernel_iter = gp.kernels.RBF(\n",
    "        input_dim=1,\n",
    "        variance=torch.tensor(variances[iteration]),\n",
    "        lengthscale=torch.tensor(lengthscales[iteration]),\n",
    "    )\n",
    "    gpr_iter = gp.models.GPRegression(\n",
    "        X, y, kernel_iter, noise=torch.tensor(noises[iteration])\n",
    "    )\n",
    "    plot(model=gpr_iter, plot_observed_data=True, plot_predictions=True, ax=ax)\n",
    "    ax.set_title(f\"Iteration: {iteration}, Loss: {losses[iteration]:0.2f}\")\n",
    "\n",
    "\n",
    "anim = FuncAnimation(fig, update, frames=np.arange(0, num_steps, 30), interval=100)\n",
    "plt.close()\n",
    "\n",
    "anim.save(\"../source/_static/img/gpr-fit.gif\", fps=60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](../source/_static/img/gpr-fit.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit the model using MAP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to define priors for the hyperparameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the same model as before.\n",
    "pyro.clear_param_store()\n",
    "kernel = gp.kernels.RBF(\n",
    "    input_dim=1, variance=torch.tensor(5.0), lengthscale=torch.tensor(10.0)\n",
    ")\n",
    "gpr = gp.models.GPRegression(X, y, kernel, noise=torch.tensor(1.0))\n",
    "\n",
    "# note that our priors have support on the positive reals\n",
    "gpr.kernel.lengthscale = pyro.nn.PyroSample(dist.LogNormal(0.0, 1.0))\n",
    "gpr.kernel.variance = pyro.nn.PyroSample(dist.LogNormal(0.0, 1.0))\n",
    "\n",
    "optimizer = torch.optim.Adam(gpr.parameters(), lr=0.005)\n",
    "loss_fn = pyro.infer.Trace_ELBO().differentiable_loss\n",
    "losses = []\n",
    "num_steps = 2000 if not smoke_test else 2\n",
    "for i in range(num_steps):\n",
    "    optimizer.zero_grad()\n",
    "    loss = loss_fn(gpr.model, gpr.guide)\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    losses.append(loss.item())\n",
    "\n",
    "plot_loss(losses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(model=gpr, plot_observed_data=True, plot_predictions=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's inspect the hyperparameters we've learned:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variance = 0.24472779035568237\n",
      "lengthscale = 0.5217776894569397\n",
      "noise = 0.042222216725349426\n"
     ]
    }
   ],
   "source": [
    "# tell gpr that we want to get samples from guides\n",
    "gpr.set_mode(\"guide\")\n",
    "print(\"variance = {}\".format(gpr.kernel.variance))\n",
    "print(\"lengthscale = {}\".format(gpr.kernel.lengthscale))\n",
    "print(\"noise = {}\".format(gpr.noise))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the MAP values are different from the MLE values due to the prior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sparse GPs\n",
    "\n",
    "For large datasets computing the log marginal likelihood is costly due to the expensive matrix operations involved (e.g. see Section 2.2 of [1]). A variety of so-called 'sparse' variational methods have been developed to make GPs viable for larger datasets. This is a big area of research and we won't be going into all the details. Instead we quickly show how we can use `SparseGPRegression` in `pyro.contrib.gp` to make use of these methods.\n",
    "\n",
    "First, we generate more data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AZjlqXxuT1akkQ5XktZKyYYRhqIfDoR4Oh3o8HuudnR19cnISZdUAyUAsd5S0vIw2T5SZ8FxiM+C8hDqZTEo3rkneLemhkkL47Oxs7XNJghqeZtBEisTk500zx6+rnkzyOTnGkj3JvJT83ve+VxORPjk5Ke2aAGySPBNOcwWYV4a4AJikjPGB+1jWdm7zfiGI5Q5i66ymEeWH3vRC2zqn7bwsrE9PT/V4PC60bOva8cseMrNzmiEW/JpjHl2eZT4P3wvb5il4tEBbSTLSPkLYtzJfFmzGlT3Jd+7cifVbXkI+PDyM9W8A2kbWUCbprLKtCJvH5rFbbFcnk0m0quNKMZd0jm21mRDLHcP2MHPHc80gs3RsPnY8HkeGdDqdRss6WUI5uH1y6Uq21xXaYfMsB0GgJ5NJdJwtZjkpNANpdECbSTJivhNjM6ZYa60Xi4UejUZrAtpXPJvtCoIg8ihPJpOo38rNfdwO2Z8B2ARleE7zhjKZq7VJn8t6DdOust02QzR9vmeVoVpNBmK5Y7jiGNkwuoyqz4PPx87n82iTAM+GV6tVFAOdJZRDimR5bh/jLEW++b1t2TBMA8zX5LgtXy/ANi9FgWaS9EzKfsZ9xmaMzQklh0bY+kwWA2n2syAI1q53dHRUulcbgKwU9ZwW+XwYhtEqLTujksji5Cp71aiNdROKArHccXyNKP/dZ+c9v+aY37yhHOa18pTRLhpvxQK6qvgyAJoAT5rH47GeTCapE9r9/f0oVKkMT5IMfTKvx8Z6m5d4QXMo8rwXqUUgV4CTnE5F21gUeJYhlreOLCVn5VKuNG55UtDZjs3j4fZJXZdEXuPMwsMnvgyAujB3yrPXaj6fJz7r7AGWWSmKeJLy9O1tM8SgWWzac8qrsrK/yhVhSZ2Tym2e0EIst4hNL//7doyixjBrBzRjMPn/zbQ9aSTdz7R7HYb+8WUAFMH2LC6XyzVDao4Fsn/47i3gWH9Z4EBODLOu4uTpo9u4xAuaQx0Ttiy23XXs0dFR5fpgm0MQIZZbRB2zurSBQ7bBtkFIik9b4ZDpdJo7kXtSCrkiuNpqxm5miS8DIC+2fp9WcESKVd4BP5lMEqt18QRQbord2dmJPme7Tlqbs67+wLMM6qQtntOkkMK8bd9mIewDxHLLqMOYpOU8NjsnC1bTQJqGuKi45XPwsrGZCi4vsm1yo5Nse5b4MgCKkrQik5Yqbj6fr62A2IxgXg92ljb7HN90oQK6S1sEo6uvFMnuhP6XDMRyC9nkMqXN4PlsGrQV/WCR6cqfnAdeNt7f3y81Nyt/D7nRickSXwZAWdj6vSt/utYvnsvBYBCrtFl3m10UESptETlg+6jq2XRNRje1v2DbqFwsE9FHieiLRPQlIvqU5f1vJaJ/S0S/df3v0z7n3VaxnPQwl90p02avrhmoq+jHcrnUw+FwraKebF+W71CVZ5mxbXTK2kYAysDXs2yu5gwGg7WsFj79o458s0WuCa8YaCpVPptJFWonk4leLBZrK05p6eKwZ8BOpWKZiG4S0T8noq8logERvUNEX28c861E9ItZz72NYjmt0+XplHk3ubkMIf99Pp9H+Zf5uNFoFBO1pujO+h2KxiwnfT/bRicYX1AHtj6RFLPM/7+7uxt7hvm9LOLTN+bYVYXTFuvsU5zI9r192wyvGGgavs9mHmeRWWCLP882jMOveKUpLSXdZDKxVre1ZclKa2OXqFosfxMR/Yp4/QYRvWEcA7Hsic9DmtVgFJn1uma1ZsdkDy0XJDDjgF2FVNLCNXzanifPNG88LDO+GoC85Ikllqst/F6eGEbOzWyrqJm0X8EMVZLtS+q3RQUvvGKgqSQV0dI624TR1ofMsEetnwvm0WiUml9dnpNFt/nfIk65LlC1WP4rRPTT4vUJEf0N45hvJaL/89rr/PeJ6Bt8zr2NYtkXX4ORVAbXJ3WaGZtsGk9OV9Xr9XS/39fT6VSHYRgL03AZT840kfQdskweXB4yHpx8Y7IBaDpsOJO8Q77I8vauVSTTk+UTDpUkirMKXts4hj0EoAry2AbbCiiXec87YczSDu5PWewpt+Hk5CSy2+a1yhpj2kLVYvl7LGL5rxvHzIjoz13//7cT0T9LON+SiJ4R0bOXXnqp6nvTSrJ4ZmQHNcvg+nh/TCNp88RK0RuGz5dmR6PRWieTlfRkpom8M1bXRqfRaLT2HeCNAl2hTK+PHEs4pzgXNJHHjEYj/f73vz+2inRycpIrNpKvmaXsPY8r0vuNQkGgCvL0L9M+8mteZS1jwpjUXp/KnQzbzbOzs1hfln9nyli9ahO1h2FYPvOHRHQr7dzwLK+TpyMndSaX8PYtG81LsTKmamdnRy8WC+syD3c+24w7ay5m87vzuXu9XqyNecpdA9BUyloVMSfHnKt5Op2ujRG8iZAzbnCIlc0jZZ4/aXOiKYCT+ieXoDfP11UvF6iPLA4prZP31hStZpvWTg6FXC6XsQJDrv7B1w6CQCul9OHhYUzY2zzPvqtJbadqsdwjoj8gopfFBr9vMI75GiJS1/+/R0T/B79O+gexvE4eQ7lcLiNjJ72/vITpm2NZHmsrp8vLNqb3mZd5eDDhjYGmRykplssV03l8fBzr0K+//npsOYpn+MfHx1ZjDUMLtpWkCnxmqffRaBT1rX6/ryeTiR6NRtEqjolrUm9OiHks8k01iRUisCnyPGtJmStkHyujHgHvG5Dhh+yo2tvbixxWsg/y+dkuslDm/5ptMh1RMr1qF6lULOsXoRW/f50V40eu//ZxIvr49f//ABF94VpI/zoR/cc+54VYLofFYmEtbysrfflU75PeJxbbacLdlWLO5UVytcc8nmOlZ7OZPjw81ESkP/CBD+h+vx+lrhsMBnowGESpdWxxzF2eJYPtxGdCLY+RolnuV5CFTnh1Rk5Gx+Ox08Cb52evlzw/h3D4ipKyvHGudsrrYBK93Zgrpj7OFXYWmdmVzAJe3BfkM7xYLNYmnj7XM20kr9TYimyZK8cybaoMxeD3bR5muSLcRSoXy1X9g1gujpy1Sg/sarVyen9sxiNpx3zatW3FS/j9pM0KpvGU52PPVxAEmoj0yy+/HBnx1WoVy85hDhgIxwBdxqdfpx3Dr+UqEHujbt68qYkoMQTDbI8r3ti3GpnvWFXFvQLbhQxtkB7brFkmptNpFNogvb/SuzudTvV8Pl8LfeL30p5Dm00zHVRJ1T/TQiy2rX9ALG8xcoZoZqhgj4/ZiWybdtjLZMZd+cYT+3ayNEErhTQb7zt37mgi0q+88oqeTqd6Op3qyWSix+Oxnk6nsR3zWMYFVdMEb6XPxNB3FYfF7XQ6jVZtTk5OMpWAl6tSPOlOS1clqfKeYhINJEkZpNI+o/ULr7T0xPLKjM1bK1dpTIeWD9Kmmc+yLXyCxb9rX5F8/pswlm0SiOUWUNVDmZZyKYsXKosxyfN9fL1d3I69vb1oWZgr8D18+FDfuHFjbfAw7wGMIqiKur0x3PdMI+q7iuPaH/Daa6/FNtitVqvUbBi2a/H1mmSIMYkGNvI8F2EYrmWIkmLULDAiV0pv375tFbdpTimZYUp6p23xyLxRVjrK+BpdFsI+QCy3gCqXGV1LoGZeYlvu0k0YftlJzeUq9nTbNv9xtcDDw8Nody8R6dFotBZrVrRyGABZ2MTELEnUTqfTKOZyOp3qfr9vLXAi25i0B6HoOMDjTr/f14PBYK0yYZ0GGpNoYCPvc8GeW1v2qaQ9PLxq0+v1vMIdzfdYBMvPcbx0lvzo2wzEckuoatDe29vT0+k0ZhSDINB7e3vRdXZ3d6PlINmBj46OSvX+JKWk405uxovZDDmL5QcPHsSWm0ajUabyu9s8iwbVUrW30iZgd3Z2IqPLm43M2H3XZ5PKa/tsCEzyfskY5Z2dnaiAkVz6raM/1r0KAJpJ3udCHueqa8A5zWV/XK1Wmoj07u6u3tnZ0ZPJRE8mEz0cDp17fZJsmu09HguweuIGYrlBpIm2KgysuSwkE6iHYRgVI5CbdqoyGq5BSC5J+RQsscViv/rqq2te8SzLxACURRkT3yzVK83c55PJRPd6PU1EkcGVnzs6OrKWzeUJtE+ss6+QMPdGhOHzrAFKKT0YDKyesE2BSTSQyFVOc+XD57lwxTtzCJM5OeV+YaaSY5t89+7d1L6Wd5wA60AsN4gkQ1PmA+2qbsdFBRaLRbQJgYXy4eGhHo1Ga0tHZRsU2/eUqWxOT09j+Zx9zpWWKgeATVGWt5I/t7e3t5a9ZrVa6aOjI621fYIt+7Ut3ZOrjcvlcs0DZevrvmOVyyPNG4bZm+baYJQGxC4oE57IJeVATnvmbH1rNBrFsluwTV4ul2sTVxbLr7zyijXW2bcv+7422eY+BbHcMGyGRj7AshqQObu1kRTawOc5Pj6Olmf571yo5MaNG7Hk5GzAkjq/uYyU1kYT08DLmCreeZ9WutNsV564rG0eGEA1uGKJbTHDac8ZG2+56mOuDJljCb8/HA6jjDC2stBJnzVzxdr6ks8qmBlHyWEio9EoJuh5g25ej1nRiQloH1WN3Wl9IO2Zc7WL982YewTMSfBwOFyLWU4LoUiavPrep6QiRdvSpyCWG4hpaGxJwM1k5r6iUX6e4xZ52ZPF6IMHDyJDxdkjHj58GNs9u1gs1q5h7uTNY6Rc5+J4xuFw6MwFLSkjLgvGFmyCIs+ZzCJx+/bttb6xWCwiw8vxwBy7H4Yv0r7ZUl/Z0k75pLDy8SzzpF9WA+z3+9EqFsdmcriIWR3M9575erlBt6hy7JYFO7I8c1nCLE1RKmP55TnYjqc930VDOG3tkbUVtgGI5YaRNrhLz7IUlD5p18xzcgeSeRzZe/zgwYOYd8cMxTA7iZlrmTsUJ1X38TRLTxMfMxqN9PHxcewaspqQr7cgr9GEsQVV4aqElaWgBz+bLCp7vV7UJxaLRaygwXK51C+99JIeDoex69pi983nXsYVmznZbZ/zFbG8ysVjDKd75DFpNpvp3d1dqzD37ZtSKGC1aHuoYuzmc8rKdjZs4jSpb/D/y0I/ckzgiaTv+ZLugyyDLY9J28MjzyP3OW0LEMsNwufhN5defMMKzM4rOycLXz7m8PAwtizU7/cjDzNnxJAGxjbTDMMXGwdfffXVmAheLBZr6arCMNR7e3trO+59S2/73tesYSy2eweAJK8AM/u3rUiAz2d5tzwLZvY0sdc2a0EDH6OeNJm33Qtb5pzVaqVHo1FM6MsJtk/VsrS+abbX7PtcJMIcYyGeu0GZY7fv6kpSH7G9Z/Pa8rPPY8JwOMzsqZbXM22qdHiF4Xq2Gxd8P832bEOfgVhuEL5Gl+Om9vf3Mxm/pDAJ3mRgGlkWl64NQWZH50pc3Bll2rbZbJZYatpljH1n0K77yN9Bhq1kDWOBZxm4yPp82j6bVlrWhJ9dM0b5+Pg4VtzD1xNmntvmeVosFtZKY1m+p2m0WSjfuXNHK6Wi83NKS3luuXFRntPcDGzGe3KBFHYA2Ao+5PlOoNmUPXbbHC2u6nsux8xyudTvf//7YwJ+uVzqxWKx5ny6e/duJExNb7Pvd0mKkTarZqadk+0772/iMSdLtc42A7HcMrJ6lm1GygyL4L/x8uxyuYw8OxxXyHXqzRmo2Rl55tnv92MDChHpmzdvxtJV8UBmtsfMdpE1Z6TphXINYGlhLEVEENgufAyz6zlmo8hCNstzZtstP51Oo93y0jvlirG0tc82qfQNp3KdV96jnZ0d/aEPfSiaIEwmEx0EQWwlSZYRTuuLsr1svJfLZey19IDZ4kMxIe4OVY3dabbITIPIpaNlH5ICmEONTLHKfXZ3d3dNJOfx4ibt4fHxvPP1+fuZm+6Tyn13BYjllpE1ZtnHW+3K/8jeGDlr5DytZgiF9NLKuCuGY6FlKIetYhEPMFlmu+bMXS49m5UHs0w2EN8IsiAneS5vjmnAZ7NZlP0hKTQo75IrG2efDBbm58uq7CXPy/doMBjo0WiUmIYrScTavN/L5VIfHx9HoRXj8VgPh8NYjLbrvAi16hZ1jN22/ifrAsgVW+mhZceOtMOTyUSfnJys2a6iKVlNBxZnxUmztShkArHcOqr2diZl4uDr2cRnUgYMs2NOp9PIcy0FPy8LZV1yMkW+GYMtKw9qnT2MBYA0XM+gfM82IXUd5zp/0rG2vio3yNoEadL3kJPKPAbR9FSzQOCMHD5e6iQR6xL3q9UqliVEhp7YJte2sQgTYpCHpImYnETL55NXUKW45rHCN5Y4DelkMyva+lzHNrbMZjM9n8+3ZjUGYrllVDljTluOdC2n8i5alzdtOBzGqv/x7ndOP8fn47La5o5fn+9mLqu64rGyeJYB8CHNo2Q+X9J42mKD9/b21pY1Oa7Rd0VJ6/xjhVzx4fSSSV5vn/sShmHkSTs5OfGaCKeNR7ZjOBctZw+Qy922sC0W2DwWScENQB7SQnyS7BOvjJaxec4WVsUrvOame7bVaZNom4gv22HXVCCWW0LVy0o+niv5N5fX1tZu23Kp3NCg9YuNEkWyXUiDyYLczFmZJ/VeURDO0W1cv6+ZTpH/bj57LqFt+1vRSV7asygnk0opHQRBrJ1ZK+mZE2Ez5MrHONteS0xxIvM1h+GLUBSbAK5jPADdJW3lyCcTRVkhQWafCYIgtpnW7A9p8djcTziDlhky1fU+A7HcErIYjzz4CrqkWXFZKbR8v5trd/LNmzfXErVzO6q+j2V+P9A+klZfeFXFjNMNgmBtomjzSJURPpT0LLomlXL51lYeOw0zJZ7P859lPJL36fj4WI9Go6h4Em9AOj4+RnpIUCnmc23u9+G/7e3trTmh5Opsls2mWSe/7Fm2TbZtYwNv6pXn4Y2HRSv1tg2I5RaRpSOldaIiwtbmteWd56Zw9TGuRdoid+jzzF1WJDMHgKJe3qITAuy47zamp0i+dvURDnUwxZptOdf0LJurNtwG3+ICvn0jr5jk8SJvKAfjynrT7/ej/s+TiSAI9NnZmXfeavRNUAZFbUsep4rPZ2T9hLQVFLMvyPGK+1ev14utOm2LEwhiuWX4Gq20TpT22tXx9/b2rDFVZg5T3wIIRTE7dx7xkGWQK+IlhvdqO0iLO3QZpCTPshTa8nO2DBuu51E+5zIuuaqJXpkrKi6vlzTYZ2dnOgiCaALN41BSRcQy2whAVmSflKtScqywFfRJGk9s3mLTHic956ad4gxYk8lEDwaDSHjLfrYNE02I5RaR1WjZjrcF/duWV21e29FoFO2g5b/ZcqFmKYBQBkVFqDlw2JbPfAentGtsw6AC0p9JW9pErdNjlm2izvfZ4uOyTGiLiEnbfgWeWOdZqnV9T04VJycRtow9aRMIeZ2uLiWDcuDnRv6XPbWynHRaTK9P/8riPbbtj5DtS1vdsfWxMHyxD4BXieQKzrY4gSCWW4LPg2+bgZrLu2ZHS1qqNPOsPnjwYG12urOzE4vB4vPduXMn0aNTFnlEqGtJl+OcfVJ6peXUTct/C8HcXdKeSfm+rdAHG9u0v8nnTIpv1zFav+jTd+/ejTbp2LzfTB1Ly0m4RAEb89PT01iu9W3agASyUeTZNieeQRBEAtK2iS9p1ZNXh7JkfbGJadMplnWi6uqrcsP8YDCIjRvwLEMsNw6bR9hWwtmMh7QVFTCXZpJ21pvVv2SMpTSys9ksEtO8ucaMaSqbvIbY9Tk5sfAdnHyENbxX20PaM2l7XXSjDHtWpadYGmHzWeTnnDPZuI4ti7TJQ97NfPIe2iqjdd14g2IUnciZdlRuKuUCJLbQKtv1fLyzad5j+Tqp7oELlxOJi5CZ40ZSpdwuArHcUpIMh+zAx8fHax01DMNYKif5OZsoNMMqbLvb2VjxJgI586xKFPoa2aRBIClu1HdwSsqpC7YLs/w0x9EeHR1Fr80+UcTohGEYK+fME2QWjUlebZtBLwuzz8mVGNt3sGUJWa1W0WqZOX6ZeyTC8EVZ716vZ/3uSe3j62ICu12kTeTS4OeabST/9/T0NNF+pGW+8W1n0nNc9LvJ85vjRlJtha72IYjlFuOajcolWZuR8Smxa85QzbyrpldazjxlyEcTOo5r9u3K/Zp0j1zL4bacumCz5B28yxz0zWfNLHLhEsJ5DZvNmMniHxIpylm0m5ltqsjbzoI+qayuuQpmLvNyvzPDRriAizmx393d9W6f7TXYHopkerl165a+e/fummd5Op3q4XBo7c+2LDdJz2GRZzXpu2Vd0dn2vgKx3FLSPMuumatviV1bXDQnNWfDLz3MZcxiq8RsnyyvPRwOY7kkeYMQV0xLK8jQ9O++LeQd1JM+l0dI2541H69QkvfVB/78eDy27n43vbccWzmfz0srqyvhVRffEvZmyBeLYP4Mfyez8qctH7RPJh70W5D3GTBtxWg0ipxJvMrKaQ3lM2+uaPpkbyo7Xak5wZZOoiJhUl0HYrmFuIz7YrGwVgxaLpeZNqQxZieRS8jSgI1Go9iyZ1o2iaoxl8K1fu65+rqv+zqrJ9n0evlmDJHvb/usuykUNX6uyafP5DJJ+KaF9JjPYdYUiLbn2LVngY+X4UMylMP1ndLaYMNVxdDcjMztuX37tnVVjM/DG4x44s/LwXlzvG/LTn6wTpGx28yGsVwu9XQ61fP5XI9GI318fBxbyQnDUC8WC+/0bVV+N/P/zQktsAOx3ELSciDLDjKbzSIPaVkeFLMj8gYjm0i3HV815qC0Wq0iQ2vLQJDm0TMNqk9uzG2bdTeJvALI9jkpxHyS+duEb9KOcZf31XcFSL7HAltOVuXqj81bJZ/9MmOp5fFJm2Tl951Op9aNirPZLAotkQVcpBguYwUAQmG7KNtjmhajbMt8U5WtSLNRMvuTDMUCbiCWO4ZpAPLsik3DZ5Cp0xCF4fMlZy4NTESx8BHbLDttqUp6suBNbi6237PI8ypXFlxlYhmZvJ/Fqhm6ZHtWXN5Xn5RSWq/3Rxbri8VCTyaTKJZStsHcAGR6lvm9vKmhfPoI/20+n0dCWXqGWVywMedYUF7iNtubRXSgD4MySbJ3da9euJ51md0CE8Z0IJY7iOycdcYb1TlIhGGoe72eJiJ948aNSChIESx31EvxIJfVpLePN20kiWwbiPnaDC6jkDZhTHvN4Qz7+/uJsbBhGM/3y88MJ++Xx/kWuEnrQ65ni1dXzDSOrvh7+bybHvQ8/dj3mU8LD5MVQ6WHudfrpe4lKKN9ANjwSeWa1U5Uic2JZoZt8Xi1Ke9324BYbjFpxTVMz5rZweXfy6buQYJDL5K8yklVjcLwecVCvpfseZNL1b4iAl6szZA3jZLP53w8y2H4IqQiKfODPN5HtKellLKlXVssFmvZXmTpZ5s3ejabrX2myqIDad/PvB88AZB5bF17CQCoEh87kqUU/SaQWbJk2JZslxnr79p/lFaCu4tALLcYlwfMlq806b9ld16XAa8y57KE7wPvOuaQDLM9aQIgDEM9Ho9jidjle1lERN2TB5BvpSNPzLLMSpG24uCqspXF0NrSrpm5v820jjZMD7pZVKhMY+8zgUzz3iHWEhQlzwpDUohe2rnTKnFWhWxrWhEk83vZ9k5UEd7ZdCCWW4bLIzSfzxM7gfSQpVXtK6ONtt3pPuWvy1ge3dvbi82O2bDu7e1Fx/gIJ2mQzfPJ5SrfyUDdsWvbTN7JimkEzM2sfIwsnsGb0MxNrrZnwyUaWUS7VoNMzw6L4du3b68ZuKSsGGY7pAe9aGXBJLL286Rxr+tGGlSHz6Qt6TM8pvuubvher8rc7z7f0ZYL2idNbZeBWG4wSWEWphD0EWHcAWSVoSrJ05nydGyTtIHGp11h+KIymjnDzpOqatsGliZR5JlyiTRbphfT6+K7gpP0bLjabhbnmM1mUYz+7u5uokfWZZx9POhNwFwaNn8TALKQ105xzG/WtGu+9qcsz21W4W1rn8vRs00OIIjlBiM7iDRmMvk+5zj2CSnYlGdZkqczlS0sfTdjSFwGeW9vb+1cJycnUQJ683vIa9hixMry1AE3ZW/mcj2fWfJzmyT1kyTPDhts3pxnFuToYpUu07vPmxOlWC7y+2Lz3/aRdSNtGIZ6MBg4K/EVvR5fY9MOFts4YIZ0wbMMsdw4pEDm5dGHDx/qs7Oz6HWv10vNZ5zX41WUIp2pzBmra9IhO71pCF0G04wl5d/h8PDQKTZkjBsvbctzNdWDB9z4PJ9ZN4Am9RPXuTjtnIyP9g15krRNIMp75kp7l3dca9PEAeTDNbF1OT3McV9uNs3q+MhiFzftuXWloTQ1BmKWIZYbhezERKRff/316L9KKf3KK6+spbJKEn51ZMPI0plsGydkRy2jPWXMgl1eep/MAbbNWF0fZLpGlmVU3xWfpH6S5Fm+det5nmJbHHVThW5Z+MRV5mXbvGbbhsuBFARBzKbKVQz+zOHhYWru9LTr+tjFIs9gWZNf13mQDQNiuXGYO9Q//OEPayLSd+7ciXK4pnlJ6yBvRS0ZG2y+LkoZs3T+XnIjlPQ8+GQd4GPu3LnTyN8OuLEZOzM3qcsbY3uGfePrTeO6jZ4diRQSvFpjiueifWmb4jGL0uSViaRVwslkshaSKNOvmqsWciXRPJ/Pd91UWBRWR8oHYrnBmJ5lntG+/PLLsaX/tPjbtnB2dqaPj4/XCiMsl8vCg25ZniIW8KPRKJbvNQxf5Kj08TjeuXMnNui2/bfbFmzp3larlR6NRpE4duUmzfMMZ/Hs1JWWatOYfcVMFVnGBBue5Ww0WZwltc1n45prJbHK71bG5APPcLlALDcYM2ZZKaUfPnwYpaaSuVC70CHMyUFZg1KZAzl7Dc0sGT6ePl7S42N58vPKK6+0/rfbJmzPk7kJxhTUfFyVwrXJgqVMbHGVk8lEj0YjqzfQ9hn+XJZ0fl27j2XTZHFma5urvba/S5skj2nSd2Tksy4LkXRt0rxpIJYbjFziPTs7i+KpuHzuYrGIPJxlLj/WiW9p4SyUuUTI5zI9Dz4xXLzsJ8NMuDwyD8KgHdgMqs0btWnB1WTBUhWuPin7XpbfI228aHLIQd00OXQlqX/yapCZkpEdHMPhcM1509TfnL+b6Wgrw5ZuMxDLDcbM3MCCmVNRsZgeDoelLT/WSVWe5bIpIkh4UJYeMJTsbSdpG8zqEq5NFixV4XOv8/werlz3ZpGiJo5Tm6bJEzWzbbbKmTs7O1FqUCk4bXnVs64cbXqClWcjOSaByUAst4Ck5SK5/GtbfjRpcocouzBCFd+1DI8hixmZ7gsGt13IPmkrCVvVprMs7dqW5ylLn/SZSPjkZffJfLNNNDl0xbdttr7jyiTFHmefTbxZ2lAWMr0sP+tp40+Tf8MmALHcEmyDvM/yo0mTO0TZbTOLF7D3oEgquqICnL/Ttqb76gKuJVz5W/KmvywT2bLb1aS+nZUs/SxLhgHe75G0nG7+nqvVKqqMKD+3jR58F011wsgNuTI1KW8aN9vo+k1tfctVrMPFJieyea+1jZNtXyCWW0DSA+zzcLtK9s7n80Z1iCoqrWX1vFfZziJipqnGaBvxyVvOEzNbufSq2yVp6zNStvA3PcJJhZlsv91wOFzz0kFUNB/53Eh7wK/TNvbZziVDObJ6bzcxwSradzAJtAOx3HCSHvysy0vyuMlkshUdIgxDPR6P18IesmCKoDAM9Wg00sfHx5GXwidkpIiYkb+hbxXCrN8vT7u2maT+l2fVpwy69FuWKUhdFdtcewXkGDkcDtfSWXbFg78NyOdIToKSfkPXbyr7s4wL9ql5sKkJVhl2BpPAdSCWG07Sg58nHVLSgNFFpNHLu4nO5pWaTqcxQ7qJSnzSyMvdzWV53WD8s1N01aeq9nTlt2RxMp/PS50EpHnP5CTbrNZmFqEp2hZQLja7KD3ASSGNkiSxa6YM5TSgQRDEjs0qxuvEDD9iT3wZFXS7AMTyFrFtG8vKXAo3herJyUm0NLu/v7+xeyjzZtqEWNEQkaZNoOrylGa5rs34VmEcs1b/atpvmRWbOCnjfibdH1614evN53M9Go30aDQqZRUHVI/5bEgPcF5HkXlOKSy5/x8eHjqLUrVhxaeKPT5dAmK5RZSxvFL1xrImDQplz5R5UNzf348mHfz/efIkZ71XPJjxYMzekvl8Hvt8XpHWxFi1Kj0ySfff97ou4VV3JpYm/pZZsH3XrBuqfM9rvh4Oh3o6neowfBHnOp1OIRpahG0VLgyfh8/J35bDJ0wPstlPXf2ZQ/DMMbnt/a7tE+0qgFhuEXmFQ9bPlRVbm6WNVVCmYDEH38FgoKfTaZQnOU/S9yz3SnrJwzCMvCWDwcA6+ck64DV5kMzTtizLqq77L3Niy30CfI6yn/WsS8FJz0pTf0tfXPdiPp9nSv0mP+sbupb2u4N2IFfhtI6vGvDEJwiCtTAbc9+BJKn/m7mN22rz2j7RrgqI5ZZRlXCwXSOvCJBebDP7RBuNDn8fjk9bLBZ6Op3GqvGZhQp8DbYU4Ukx1XJz4Ww205PJRE8mkygtkvn7ZBnwmjTBcZF1AC/qGeb35EZY8xxVZG/Jusko7znaiO/Yl3QPfH8zCIZ2k9av5XuunNlpfcknH/em+11ZtrvNE+2qgFhuIZtMP5O303Ab21jpyjSo7JGQJa2Xy6Xe29uLZcAIw3j+TtegZb4nKxb6YPOu2Twevr9dk0JnbOR9Fn0/l5RblScm4/FYj0ajyjd2pbU57f2m/5Z5sGV/MSenJq775CMmku5xF+9v1/D5jc0+n5ZfOW0MadJzUXS8bJu93hQQyy1jkzO/vKJctrGMOMNNY3qiFovFWuzzcrmM4tXSDHGSd0NuGMwSUpMmproy4BX9Pj5ZD9JEFZ/DDHmp6t5mKYzQ5t/WR2Bw/5MTFS74slgsvHLazufzWHniMHwe0rS7uxvFr8rrZxHXbf8Nuohv+ESaZ7mu9I9lkMd2N0nwNxGI5RaxyYG6zNkpp2Bq05Imf4+7d+9qIlrbFMK7481Nd3wMDzBJg5bpUU77PX1+/64NeGXmDJWCid+X8YvmJIl/Sz7Hzs6OXiwWa/3C1Ua5EuHb9m3yavp6eXd2dqKQJ55cpqWBlPeRs1nIYhT9ft+6mlNW3DhoJuYzxtUZzZRvq9UqGts3WVioDPB8VgPEcsPIuzmlis1seUS52Q42dk2rFugDC13eHT8ej6N0cXJDCE8GTk5OYveKl4pdnmWf0ruSLoilTX0H2zNsGjszVZLZFlc/sFXtsh2XtXjFNnotfQw7jyG9Xi/y8PsIZZ4csSAajUZ6OBzqGzduRKm+8t5fxDQ3G98J7NnZmQ6CILbCwHn0ZQpBWZ+gyf1xG8eQTQGx3DDyPuxldpKyBE3TO65P6jD2KLBINr1RbMgHg0EsRpt3Rtt2WTf9vlTJpr67b6qnpOvazsGG1BW24fv3LG1u02TIB/N7ynAJ17E8QeHJa1IaN3NVgPsji2QWylqvP3/wLLePpH6aNs7IZ2UymeiTk5NotYlj5eUekab3x20ZQ+oAYrmBpA3GZQiBTdD0juvrEWTPFBHpXq8XeRfk59ngs5hOqvLV9PtSNXWLjaKx+C4D7DpvGV5I3/jeNjxX5sRxZ2dHj8dj6xI3ixj2KPOkdTAYeG22NFcDiEjfuHEjFgMtJ8i++xC2caLbVNLGcZ80i3JCNhwOY8/mtlS7BclALDcUM0ckkzagSy9NGwxn3diEm5kSiL3Gr776alSgYDKZ6Ndeey2Wuu309DQ6FsuzydS1jF1EqPuuRMjnyDTYMntKnnbb+rzNk2obJ5pEGL7INGKbfMrjZHwx97/hcLhWVc/1XaVQ5nOMRqPUlZ9tiBvvCq7fzGeckRO24XC4Vu2v6xMjPNN+QCw3EOkNyTKgy7/JSkX8WZSujOOz23m5XOp+v69Ho5GezWZRHHKv19PD4TDmhU7zkmVtl6RLg1ddnuWqvIKu8wZBEOu/ZmhO3uskZe6widCmkpYCUevnfWG5XMbixHki4LOSFobPq7bdvHlzrSrfgwcPnHsKEJPcPszfzHecCcP4JnR+1nZ3dzs9DjNYLfEDYrlhmA9qUlUgU+TZQgc4vrINmxM2jbnMZtvtLL120vvAS3WmV2+5XEY7qaWAybJpzzfero3UOTBXNQlJ2kxUlmeZ8ckHKwup5G171YIgy4TJPFZmNZErcK4QDD7enFScnZ1Z72ddk7kkuj6BLoJtBScIgljRJq7KKH97/q/MaMQ2gEPpmvDbb4ImPvNNo3KxTEQfJaIvEtGXiOhTlvcVEf3E9fu/TUS7Puftqli2DYq2evNJBoRZrVbRDvLxeIwOYMAeJt/dzjIu2RQieZfCXeLRJ96ujWxasDZBTJiCLG9b0wwaX2c8Hns/N3VMXrJc03Ys91le5Tk8PFxbgfPZG2C7n031sjW1XU3AXLGR6eDkeCpTP/L4alsZTAoL6jJYTUmmUrFMRDeJ6J8T0dcS0YCI3iGirzeO+XYi+vvXovkBEf0Tn3N3VSyb+AzoctYsP7dcLiMvU1pe0m0kS9J56VlOW+LOOkt35Wq2LVMDO00VE3kEmWu1Iakapnw+ZT7hLIJ5UxOzLJMF17GLxUIrpSKhHATBmvhJwvUbcHiHbSyte+IF75+dtL0BPL7KAlAckiifL+nwkBOqun/3TZDl2WqyY6JKqhbL30REvyJev0FEbxjH/CQRfZ94/UUiel/aubdBLCcN6OZgLuOR+fV0Oo2FGGyiXG/b8BkkbB4HXy+0j9ANwxebmFiw80amNuanroumiYkkUZzUVtvnkrKrmOOCeR2f/t02r9LZ2VmsqA/v8fBdOvfZrNm0iZfW7fud8pBXjMl7Y27S5pjk27dvY6XVIOvz3uT+USVVi+W/QkQ/LV6fENHfMI75RSL6T8TrXyOie47zLYnoGRE9e+mll6q+N7WTZdAwja+tRPNkMvHeQb4N+HZ6jmtL8zZxjKr8LSaTid7b20ttx3Q6jdIWTSaTaKKzjcuBRWiSmEjrv0lt3aSnp2mTDB/MNttC1co8v7wnbYjzbjN5xJh5b8zwCh5fOe2gzwbsNnhQy2hjnnNsy7MoqVosf49FLP9145hfsojl19POvQ2e5ay4ZtYMC7xbt27p+XyeWL1sGyh7MOTYObMwSVIIjDQEbPBv3Lix9plt+23ykEXg8NKtmflEZouxHZPld8iaas5kE8K/jV4is41Jm6CLkLaZsug9y+MMadPvVIQsYsx1bzhOeTweR+kGOSTRJ1ynDfe8zjY2yTGxCRCG0SDkDl3+Lxtr8+8mWQYXuRGoyQNBG3nttdc0Een9/f1o08lqtdJHR0fW482Ngfv7+1HaIuBPmtFwCSy5KcwMrUmqwphE2mZPNtSusIkqsmiktVXS9ImZucQu709Z41jaeFqGZy2L0Gnj71QUXzGWdG9438fu7m4sJJH7XtFNtU2gjja24b6UTdViuUdEf0BEL4sNft9gHHNsbPD7DZ9zd1Esy4H/1q0XeVrTNq9kGXTlQ47qROUThmGUgWR/fz/TEiL/vmZ+bZCOj5gwB3hTkHLaP/m3IAis5a2TMMWvmfc4TUyXnZ+5q/iGR5mfSXpO5GYxOWmyrQ6V4VnbRtHhQ9p9ydLfk+oV+NAGD+om29gGj3sVVCqWn5+fvp2Ifv86K8aPXP/t40T08ev/V0T0N6/f/x1XvLL5r4tiWev1Ds67vZOWGH29DraHPEtOVvACl6F+8OBBVBabrvNc+3gifQ00KIZpVGy5ym0bx7L2EWnsk/qYTRSk7e4Hz8ljtH1WIORmStNzbU502OlQpNhTG8TYJvH5XdOO4QwYsj+Zm+B9+pOrfzbJy7/pCVfTvv+mqFwsV/Wvq2JZ6xeDJy/J83+LDqbmQ85eL2RcyA7fO5mmi2PigiCI5WRO8wjm8ZB1kbIG4bR4fZdnOQxDfXx8HAujCYJA7+zs5OojvnmPXWIJIiqdPEIh6TNpExVbv5evsz7DXfIsV9V/XXsHbBUc+bNmERJ+nWVS4xLkpmOjTs/qtnp56wBiuWHk8SwXuQ46WX7kEvt4PNa9Xi+WCP/09FT3+3392muvrX3OtlxY929Rt8egrPtgO49PPPLOzo6eTCbRpIf7niyTnEWQ+eQ9domlLomoqskzqUjbvCdXF3hDGMP56+UESgq1rCFxdff7ssjyfcra3Gj+jvI9Wx/MQtENupug7jF7m4BYbhDmzNU3ZjkP6GTlYFb1Mwd2301iTRh8m2C8y7oP5nlMz70rG8bx8XE0Aer1eno0GsW8UT59hK+dlve4DZ6rplO2Z1nrF31Wri5kCV+T50/Kj93FMdj398g61tjO6zPR5PzKVazOYOVnu4BYbhBFsmGAzWN6ljkmTv5WWr+IP04rmtCEwbcu0S7vF9+Hk5OTQs961vtp81jlKV7gK4Jcxx0dHXVORFVBnsld2mdsnuVbt57nrecqm7xKkdSf5TO8LRMffp7NfQBlhaDY9hfI+yonJnzscDisJMywCc4NsFkglltEFz0RbYQnMTJWcbVa6eFw6Fxyl8bXRtbBt8pnoQ7RbnpVi2YEyWPMqti8BarDJ7OF+b6ZS9v2GX4GORf9arXSy+Uy8lL2+/3oGNtqn/ns2WLjuwiHPcgUbWnhD75jTdpKkdbPnRL9fl8HQaBns1lsDwnHN5dx7ze1Agd73ywglhtEWudowjI5eOHFWCwWMXHFRtX8vVj4ueLObb+rGSfJf6/6WajTY2IWl8gbdlTk3qR5rORxMFrNpqjnmVeOWDBzFbh+v79WHTWtX5ZdYbCJyPslPfBZQiuSjvP5HYMg0ESkX331VT2bzWJpGMvqs5sSsbD3zQJiuUH4dA4s/zQD2+9gG0QPDw9jHmXbb2r7HBvnTT4LdQ/OZ2dna6IijxFKMmZ5vJEyjZ8tzR+Ec3MpumLDE1cWyPx8yrSO8jNydYKfCX5+2jRm5xGEWcIwsow1WdpydnYWjbn7+/vRpLut/RP2vjlALDcMn87hWrrCss1mSdqJrfVzI8lZFaSnWArrpN+myLOQh7qfn00YhrxGmo9jQ5y3wAHYPNxH5vN5ruebq8DxigeHGOzt7cVWlvj/5ZK/z/NWd7+zkXfi7NuHq/rOfH1Ot+oKe0uiab9HE/ayAIjlxpHmXUsajOr2DG4Trt9BLrsmVWHz/W2SBsoueR02+ez63DebB5mF8uHhYWfue9eRv7UZQ+vzjLn6cxja8y3LSo1aZ6s017RxO6vwle1eLpd6sViUtgKT5T4W3ffQpN+jS2N824FYbhhJcZs+nZiXDW27sOFhLoe030HuhJdwaIXvwLdNE6OqvTnm+aW30YZpeE2h7NqwiX7WHGx9RMbUZolfdoXfyMIYRaqhNlUU+Xg1ue0yVaKM9bbln86Kr4feVgnVp4qq63rbnsoTvABiuUGkzYx9BYVpyNHJyqVIsvqsu79dA2Xe9GSualhdF3jy/oWhX7EC/szXfM3XREJZ6xcT2ldffTXXagHYDK4+wmEVaX3QN/ad+/RgMCiUpqxpy+1ZBKPt2LIFp++KUFmT7rp/j6aFg2w7EMsNooxcs+ayYdmV/4Abl8A1i1MkpSQzc2rzefLm2DbblDccpIlkNSbs8ZJL5WnfnyeeN27ciDxlXOlvuVyurQSl3UcYwHrhssemqHNtFkubFPPzMBgMYlkXsvapJngybe3J4tW0icuyBWeW852dna2lmOPVAN/CQk35PUD9QCw3kLwd1RzQ0nL7gmL4em3ZQJvxjTavZhVLb+bz1JW8r3nulc2raIol/l2lEJ5Op7rf7+t+vx/LhKC1zpQWDEur9WH2u6R+yMcn/Vb8fOzu7kYTqTQB7mpX056JrBkozDGF02hu2rNsHi/T15mv067TpN8D1A/EcsNI6qhZ0l5JD3OemC2QTpZBNYtHqyyvhmul4ujoqJQUbU3Adq9c/cTXeLOIGo1GkadQFjmQcc55fit4reohT9EZeayZ+1ymKTs9Pc0d4tT21QZztYqzAKWlvmSq3ATJAnk8Hq9tvnS1o6xVPdAtIJYbhs/SX9qAgZnx5kgSPmmbypJ+6zKWL7ltZgz8w4cPSyn+0RTSUvjZPEppfcKc3HDFRo5J5RCMvJuJ6o6H3HZ877/MTiT7Cwtj2Y+4JLb53HW9AqTNs3x8fJxYKdH8u8/mvbwTCv6tfTcqwm4CGxDLLcPHK9V2T0XbsBlec2d2GMaLG0gPlzk4p4VJZPl9TYPOFa2CILBuIm0brv5g/t1WHjetT0hvvHlu6XmW1/MpgADPcr1kuf+u/nN4eLgW+8+x7L4V7LpGkQlgVX0ii2e5ynaA9gOx3ELglaqGPJMM1+C6XC5jG8IGg4EmoqhEtmvHuC09lTloZ/GAmHm75VJx3k2kTSHtPrgmMfy+rdqauYpzenrqLHedJyYT3qt6yXL/XSszZlVOefxyudTj8VgTkR6Px7kmaW3Ed4Utqc8l2bW8Y3OemGXYV2ADYrllYOZbHVmFTNLxYRjq0Wikp9Opvn37tiYiPRwOY3lHeaCXg7OPUXBtqMkS/9yF5yhPCj/zN5IbvOQERx4jK7KZZDWsWPWplyypFG0x/4eHh3o6ner5fL4muvhZ4XzLHOOcdw+Krb22Y+ombdw0+5wpYH1W0/JMMvNkw+jCuAiqAWK5RcArVT1ZBkubIVsul1GsHm904dRjvERr8xJnCRfgz5ixlL4Gxsd73TSyiAZf4y2XyuX/m6n+TE+YeZ0k73OTRA1Yx2dMlf1NKaWPj4+jFSMWfavVKpoc8/MkC3OkTdzSrt3kvpplg97p6Wl0n+REX8Z2u75j1UK2Dfca1AfEcotog5ehC5QRe8cGlMXyzZs3I0OaZCx9N6JxLOX+/r4z5tj1vBwdHXl715pCFkPm00/kbyz/XxpkM/uBPI95/S7lr94GfDMHmZ5g3ugpQ6x2d3e1Uko/ePBgre/y5Ms1pvgIwK54O2XYF4eqnJ6eRptpzftuG3+qCpEokpMZbAcQyw0CYrh+yjBMbCR7vZ4mIn3nzh1NRLrf78dEqfRCy8/yUq6rZLmvZznrd266RyWPFz7tPNKzzN85aWNf0hL6arXSk8mk9aJmGzCfcVdO+rQ0hPv7+7G4/6RjXc+FT+7vtsfRyj43m830dDqNNt1xeJp5fNJKTtn9qy1jIKgPiOUGwR3UdxkYlEuZA+bu7m4U43jr1q1oU9BHPvIRr3Oz8eYSy3z8arXSR0dH3jHLvpQlRLOSNEG0vSc3K+b5vcw+ZRapMMVz1gIubRc124KM+5cb97LkpOdncX9/P9UrnLSalFZVssme5aw5kmUf4/s3HA5j4Wm8d0Ce10zLWIWYbfJ9BvUDsdwweDAZj8cxI47OWz1lefbDMNTT6XQtvVQQBF6eYP69WWCz4GbjXlXMsS0coWpPS9J1zPdspaWzGjjXznyegPCyOV9vMplEE58kz59sO4xt80nrY2m/nfksuj7nmzffNu7LdjbV4+nTPnkPuJ/JVZjJZKJfe+21tdUeeU4Oiaq6YAgmu8AFxHID4Q47Ho9heBtK2pIrD+CmEU0rjWwaGzbmd+7cSQwBKGIwXNk1yi5X6yJJZPJ7Zj5oeZ9ksZe9vb3Ykm4Yhvr4+FgfHR2ltkFu0uPzB0GgR6NR6uS16aIGrMN7Cl5++eW1CnRJz4sUb/w6z+pOWtEi2zF8vSatMmaZJErPssvTbO4dyLopchPfA2wfEMsNQ3ZYTkGEWW7zcA3aSeELPoOxbeMRxzzLeMoyjaitXC2/3pSnJek6MoZYIicnHAs5Go00EUVlqqfTafTaBd9LWbVvZ2dHLxaLWHaM4XCoh8PhmtfLFTLSNFEDXlDEs5wl/VzW9rRVqGUZJzjMQn5XDrOw7R3IsykyK5jsgjQglhuEuSxnxrKBZpHVo5JlMJbeqjTPqnydJ9a4DZ5lWyy16dHjPsOCmTdYplUnlOfhCep4PF4rX8yer93d3djn0DfbRxkxy4xrVcLX09x2oebqv0nZeEwvspk6zrbxVlL2JB6TXZAGxHKDkDGUUjQnFUUA9eI7aGcdjG0hHK5NLtKgFDG8VcYs+4StmNextUFuyLPdozAMo+wCvPnKBz73cDi0bjritrCw4jRjyK3cTsxny5UNwxcO6bDtL+DnISlenv/frGrXdJIm7bJvnp2d6SAI9GQyiZUMn06n0QqO2c9deZeTJtCyXW24f6A9QCw3EMxy20He5UDf3zdrvuAi7araACUZVVd+UzMftHzP9f2Wy+WaZzkIguhcrg1CsvIapwMbj8dW0S4zlbTZI7jN+OZZzoK5v4BXKmweZw75afsm7rRJMAtmvjcPHz6M9gKwYDbzxCeNe2ZO5jB8Hj8+Go3QD0GlQCwDkIMinteyvLZJolhuFkoTvZtaBna1N8/1XZMEFspBEMRes5E2M4rwf4+Pj6NNRuw55qXhJGGVNbUcaBZl90XeXyAFs7k6JJ+vpFCDtsP3hCefh4eHsfzx0pvvOwk308qFYRjtL3D1QzifQBlALAOQg6IDcF6vtPn5pPAFVxqmOo1JGZt2XMeenZ3pvb09HQRBbNPfgwcPIs+yGUqRJKA57MUViyrPh4247aOsqm1h+DxmmZ87Fsyvv/66dWOvfF66nqrMzEVtFlLKM/65+n/a2ALPMygCxDIANVHEUMr8orKIDS9THh8fR8ckebA2KZTTBLHP/fA1fK5z8d/Z2zWfz6P7J+NIWTDxUjq/b/MUompfO8kjomz9Zblc6o985CNaKRXF5X74wx+OVji01laR2HXPspmL2hV6kUe8mv07bWwp6pwAAGK5gWDZqPuUNXhLMcwibzqdrnmTbSV1ZTs2FYJhik4WqlJ0yp3xJlkqhrnCPcxQizTPe5nhI6A+yihR7vrNl8vlmhh8+PDh2oY2FolhuF49suxnp0o7knZu9rab6Sh5/4BtY25axh5bP+aY8CITaAB8gFhuIDDC3abs35cF83g8tqYabILXxWbsVquV3tvb08PhMCYizA07WXDd26RQCxbM8/nceu/Ozs6shhaT2nbhejayhtEkhQGZHmTe2MahO+Yk0RSYZT47VdqRtHP75qJ2beJ1Vcfk+8dpHeUmyqR7yZ+fz+drpbTRZ4EPEMsNBctG3cC1bGt6TosO2CzmXJkxNul1yeL95VLS/X4/ijGeTqf6pZde0nt7e4nnyHLttGwY7HnnkAvZRmzi6w7muJr3t/XJQsPC+e7du2viLGtcdF6qtCNlnNt3fGKxPZ1OoxWh6XQaTTqS0qvKc27Cow+6CcRyg8GyUfupwrtjCkJe8uz3+2ueZR+xzgZkPp+XYjiyCvR+vx8J/eFwqKfTqZ5MJtY8x0XblrYUz4bUFFNY5ekOsiKk6eWVosolZm0i0XwubFkv6niGpLdbxveWJdSljcq70uIjus1VgJOTk7W+6rqftvGyzPEObAcQyw0FnuXuUPZvaRp1WdI5DMM145z2+So8LWnfWb7P7ed/nOuWcyazqOH2FfHKuUSN3Gw0Ho8LCwDQTMznjvuM+Xz5eCnl67TKkmVs5ktbNTH/zt5YW+YXn+v7xCXbvPR5JgU+jiH+Lvv7+1GfzetQgiMKZAViuYFU4Y0E9VL24MzPxHw+18PhUB8fH8eeF/Yep3nHXDF8vrGESfikcgrDMOZZJiI9GAyiwg2DwSDyJJnCPitmhczT01M9Go30YrGItW1nZwdepw6SNK76Tmh9Jk+uY1ybbIu23yVSzfh83tiaVv497Xo8vmTNd5x2naye5bwTEDiiQB4glhsIvFndoqrB2VaeOm1JWT5bcjnaNPZppbaLfGfZBllx7+bNm1G56X6/H22+Y8E8GAxyC2XZpjAMo+/OVfrM922vQbtJG1ddk7syxuO8Y4BZInu1WsVCCMyc3/L8Pn09b7uXy6UeDoexFZnZbKYXi0XipMAWEiGz37j6nByT5N6GtM+5vg/6OMgKxDIAFVLV4Cw9wxxywYZnOBxG2STSvFE2b5M8ZjqdWvOiJhncLN+ZU91xujv2HN28eTMSxnLzIht7H/Hiik8eDod6Mpno8XgcE9+YpG4vSWK2aB8u8vkwDGPhIrPZLJpQ7u7uxs5TRsEfG67z2kI80ry95nc3y1fzMa5sGFk/p/X6hMN0IKCPAx8glgGokCoEmOk1ljHKLDaHw6HTYPnEMfI1uBrZ4eHh2rXL+M6yqIr0fu3t7UWhJLzhbzAY6NFoFBV+SBMfNpHCkwnTIw/P0vbiI2aLCM6kNGo+4k32V47v7/V60T6FpPaVJfRd31tW6PPdyJh2zrIzCMGbDMoAYhmAluFayrx7925kVCeTScwbZHpX2MjN5/PoHKbh4WOkYDaNTlkeGZsB5RANpZQ+Pj7Wq9UqCtkIgsBrR7t53sViseb5gmdpu/Gd3JW178Cc7PpssOW+2Ov1osmea7Irz1Fksp4mMvk1V8Pc3d31FrlJoRpViNui3nUAIJYB6ABy4wsbYJlGzuaNNsMQJKb3+fXXX9dEpF999VW9XC5jBpqFbVkZKvj1YrGIPMly+fm1117Ty+UymhCkxWGaqcLgYQJZKUNsuarQjUYjr9CF27dvR7H7MgNFGZtx09prnlf20Z2dnVg4l+klt63upG3Mk/ebi44U/X7IgAGKALEMQMsJw+dV72TuUSliTS+WS0Sb5zNL1bJg7vf7McOYlqouDR+jzN6rfr+vx+NxLMbZjLl2iRLeNGi7DgAuyvB02jbNcnW/k5OT1HhjudlV9r26Jnv8fWTf55WfpAqiWXJOlznJhWcZFAViGYAWYxqOtI0vtuVPUzCy2JQGnmMs2cCzaPUpglJUkMq4SM6B7LMM7SpxDUMJslBGDK35THI/Ojw8TPS02kpkcxEdXuGR1yy7OmhSf7alYpzNZmvX1/qF8J3P517jgylui1TRrCKsA2wfEMsAtBgfYyb/nqVyVRi+2Imv9QsP8+HhYSw3cp7y2r7IcBBOF9Xv96Pru6qScdttXil4kkFR8jznfIzcA8B9ktOn2SZ+rjALs3iKbZUnqV1ZytKbk2ezPyWFOGT16vLxZhpMc5+FL8hyA8oAYhmAEmjigCwNnTTKrvCLpHOYMYm8K384HK55srlgQdFNdFKsSyEQBEGU/i0p/AMxiqBK8sTVyk2zpiBk8WvmTvYR4LbS22ni1Ffw28YA/vt0OtVBEKx5gZNiln2z6chjOcQjrc8DUBUQywCUQFOX+rgdrkp9PgJWxg5K0cpV9mzeLFkyOu+9sOVH5SVoU2C4DDxiFEGVZImrzZKyMUt/tU0KfQuscH9OW20yvyf3qyAIYgLaLB9f1InA7ZObkZsytoLtAmIZgJJoqkCThk7iY7TM78QxkabBldkwpIEr2xOUdenY9hqAMjD7hoyrleFLWj9fben3+/r4+Dj6LJeHdqWoS6ou6WpDmmfZ1jfkxNbne7J3/PT0NBaawQLf9CwXXV3z2WcBQNVALANQIk1b+k9aQvVd4s0iOuUxfC9kAZFN0MSQGNAtXH1DpnCU7y8Wi7X+Z9sMJ4WpufHPNkmVpaK5gI+cnMqVGNs1ODRLVgKVx5krN6Z3nP+eReDnuc9Nc0CA7QNiGYCSaNrAbhorl6Fz4SM6XdXJ2Mgm7ZDPC8QwqBtXKfXpdOrM4ODK6GCL0WWhKosL8fssmmXmG349Go1i3mszhpgxJ7IyvEpuNPSJqZbfyyeHsi9YIQJNAmIZgBJo4sBuM+hyCdX3M0lC1Pa9s+zIz0PavZYltOVnihROASCJNE8z9zfbypMpgqUINbPXpMXw+kzYw/B5HvW7d++ueaFHo1FUCdRchTL7lNbPPebD4TD2vWU5+SJgUgyaBMQyACXQpIHd1Rbp7U0ypHlDL1zLxXxMmfciLS7TzPwhXwNQNi5P82Qy8coVbD7PSSWsZciD7Vw+adxcOcjNMJI0DzFv8DVXr+7evVu7swCAMoFYBqBGqhDZNsFrisUkEZwnnKSOWO00UcDVCsfjsR6NRqjeBzaGKwQqac+AfJ59JrwyRMO8rqvvuqpb8oZEuVFPesV9Vpfy7IsAoC1ALANQI1WFb2Tx9sqKfXyM9DBlzZixCePoc00WH2WVzAXAF1csv5m1xcxH7LPqwzHFsnS93CdgPuOy78v4aFlMRHqCOUyD9zcklbPn8/F5uNAKf6/VaqWPjo7Ku7EA1ATEMgA1U5XY9PX2mkuznDv18PAw5ilK+qyvCC3Dky6vYVYVkxsMWUwMBoPIs+xK7ZWnHQDkxebhTStGInONywJBx8fHWimlj4+PE73RMuaZBTbHP8uVFz5mMplEWTJcIUzyfOxZnk6na7HUALQdiGUAGkDZYQxZBTgff3h4GHmIbLGTJmVsCMxqUJOEBguJ4XAY5Xxlwy+XluFpBnXiM+FzeaHN3MYsfJNyG8vxgMvGyxzoZnukt9gMwzD7H59vPp/r6XSaKeMOAG0BYhmAminbs5xXkLJxvHPnTky4cyES8xp5vbBVfV8WDovFQo9Go2gJmZehF4uF94YrAKrG1g9M4az1i5R0ZqgU99fhcBj1z6S+LsWvLPTB2WOk4ObMGLbKfjahL+On0zLuaN2sDdEA+ACxDECNVBGznMcQmZt0pGeoijZm8aT7fB8zbyyLAS6SwB4wU1T4GHYAqsLsB2ZIlGvTnPm+zO+cFO8sC5HISaMMteDVmaRwCnk+mVvZPLdrjKhiTAGgSiCWAaiRJnhYTANs/lcazDKLDWQNEXEZVtsSM+d6ZYNvprjSej21Fww12CSufsB/39/fXytTf3Z2Fu0p4AltEAS61+ulposzY5Zlvz4+PtaTyURPJhPd6/WimP6k0A6zah+fezgcRvHU8rrm53lfgVmqG95l0EQqE8tE9JeI6FeJ6J9d//cvOo77QyL6HSL6raTGmP+6LJabIKDA9mDLhiFf83NXhjfYtWPfVzC7hIVcspYZMMwCDub54NkCdZD2/PGKx/7+/tpx0+k02lvAzzjHDKelizOzYfA5ZbVAGdNvZtExK3RynDIX/GHPtPRKm31e3gNbhUL0QdBEqhTL50T0qev//xQRnTmO+0MiupX1/F0WyzDkoGkU8QbLOExZpSzJa2XDJtZNUb5cLmPCgUXHfD6PnQsTUlAnSc+fWZbeFsOslNL7+/taKRWFHvE58tgKKVx7vV4s24Y83/HxcWzFhj83Go1igtxW6tu26VDmQkfRINBkqhTLXySi913///uI6IuO4yCWLZS57A1AEXwnb6YAYGPoKp+b5Zn26Q82LzN25oM2weLTFqPMG/FkVpe7d+9Gnl15jqypGDnWmM87GAzWymlzmFO/34/Cl/hzZsiGnKja+p/sq2Y4BwBNpEqx/G+M1/+X47j/nYh+k4jeJqKl7/m7Lpa1rqcqGiifOryYPtf0bZftOFuGDLn8yudib5Vv+VwbecS6KTKwOgPyssn+m3YtXjmRG+pMsZznmpwNQ27aWywW1hAs2a+lV1tier/NnOYyHERes8j3AKBKCollIvqHRPS7ln/fkUEsv//6v/8+Eb1DRN+ScL0lET0jomcvvfTSJu5PbcCz3B3qCKvxuWaRdrk8YEEQRDvz5S5538wTvsI8TayUdR4AmhQWJ73Aso8VbQt/Jxkmxd/R3Ai7Wq30eDyOQjZMIcyT5iTPsrxmE+4rAGnUHoZhfOa/JqJP+py/y55lDCLdo47Jj3lNW8lrNmx52uWKrZRLuWZIxO7ubuaUUlKUy+Oyilz0K5CXpjgv0gqGFD2v7BNh+Dw3ufQM8wZaHjOm06kmotikeTKZ6CAIUmOWsW8AtIkqxfKPGRv8zi3HTInoz4v//1+I6KM+5++yWMYg0k3qCKsxjapNLBbJNWzu2mfBLOOUwzCMduyzYPcRzGbxkDJErjw3Sl6DLDQlLK5q4Z7URzgMROYrn06nejQaVdJfAWgKVYrlf4+Ifu06ddyvEdFfuv77+4nol6///2uvQy/eIaIvENGP+J6/y2IZdI+iBq5IoREzj6lNiBaJJeZ8sFwi2+ZNNpeKk9p+dna2JuDLzInMogclr4EvdXiWbX3eti+givbICn9MGIb66OjIOg6ZFQHh7AFdozKxXPU/iGXQFspY/s96DldM8Wq1igxbEbEozye900EQxIyljFv0NZZp4R1FPHtlThbAdlBX+E6VIUlp1+WUbmbxEtt3bkqICgBVArEMQMWU5WnJYpRkrlPp6R2NRtGmuyKG13b+4+NjPRqNYhUAZ7OZ3t3dte6IT/qOZjlfMwaSr5nl3lYRhgK6T52e0jKFqM/3MGOWXUV9bMfbXgPQFSCWAWgRWeMmpbE1d84XNWy2vMqc/ok3Ag2HQz2bzdaEtc85+bseHh46l56zGGvXsjZKXoOyqEJYlxUr7dNXzPbztc2iPq7j+bwIuQBdA2IZgJaQ18skDV7Vho3bOJ/P9XA4jBn5LNfKshEv732BVwyUTdZnKi3FoVz9kBPGou3z6StVhFdAXIO2ArEMQAvIK+zqiCeUFbmqLEJiu2YW7xsMN6iCPIJUPuu8AiTDmWxZJvLi01e4Xba8y0X6CCaooK1ALAPQAtKEXZ6d8/IzMs+q9NimGUVbKMZ0OtX9fn+tXK6vQcwqYrHBCDSNLJM32/Mbhs8389k24RaZzPn2FVfe5eVymRq6kdZO9FfQRiCWAegANo9N2gY+22Yen93vruvyOYbDYZRfuQxvVNbvDQMM6iSPGLSJ67LzOle1OrWplSAA6gRiGYCOkMdIy8/IMrp5Yn/n83mmfMplgFAK0CTyCEeXZ7lJ8cJp4rbuWGgAqgZiGYAOkcdjIz+T1+PTZE8RBDXYFHlDEvgzXCFPTjo5Y0tdotJX3GaJhcZKEGgbEMsAtBhpnNnwnJyceBvXsjzL0+m09PjKsoCBBkWocrJli/kfjUb6+Pg4es2b+1zV87LuK0j6nK09s9lsLTuHKxTDNxY663cAoG4glgFoMdKYZt05nyVm2WXkeMNPVTv3ywJLvyAvm55suZ7VojHHPp+zebo5d7o5CZb/xWQUdB2IZQBaTl7PbpZsGD5GlJeLs3i2fcjqjXIdz2W+mxgqAprNpidbrpCGvO2wfS5tAmyLobYJYniLwTYAsQxAB9hEzLA0uK5qgFWUjs7qubIdnzfEBABmU3H5aYK4rH0FSf3Kdg1+fz6fr5W/hjgGXQdiGYCWswmvF3uPpBHlPM583cVisSZIyzKiWb+jLRYby8QgL5vyLKdNDMv0LLv+Lv/W7/d1EATRebj/37hxA/0JbBUQywC0GFd4RNleH9M7y55l9iQfHh7q0WgUhV+sVqvoNW8OKkpWj9omy3yD7rLJmNykkIaqYpZlvzLfC4JAE5EOgkCH4fPc7USkR6ORns1mWKkBWwPEMgAtJs/u9TwxhmH4YgMge2s5xRUL5ocPH+qdnR09mUz0ZDLRw+FQj0ajUgxpEc8yjDkoQlNicvO2w0eAcz+RexAYFsy9Xk8rpaKCQyycfSevTbmPAOQBYhmAluMSzPP5vLSKW2YYxsnJSUyUr1YrrZTSh4eHmog0EZW2ya+MmGUIZgDiZOknt2/f1kSk9/f3o2OTxpii1wOgaUAsA9BAsnhhbEYozeuTx/PK5+VsF1xKm9vFHuZer6eJSI/H41IMYVnZMODBAuAFvv2EJ8L7+/taKaWDIMgterHiA9oKxDIADSSvN1XGE5dRccs8vyuf8mq10js7O3owGGillD45OVnLmAEAaBcslHlivFqtohhmSZbJaJOrfQLgAmIZgIaS1QvDRkh6dF0iO+u5XZUCp9NpJJg5G4YpoIts8IOXGGw7dfQBvubR0VEklJfLpV4ul1E1wTztgGcZtBWIZQAajK8Xho2QTw7UMmIHZbvMal7ymkWNOuIcwbZTRx+wXdOVgtG2KdDW79GXQZuBWAagofh6YbIaoaKeqk17h+CNAtvOJvuArOYpc5WzKM5S3c92XvN7YZUItAGIZQAaSBYBvEkjVJd3CHGOYNvZdAXBMHyR/UZmtkmq7ocJLegqEMsANJCmemHqaBcMMdh26ljN2dnZ0ePxWE8mk2ijblI7MKEFXQZiGQDQWBDnCLadumKWx+NxrLJfUtl4TGhB10kSyzcIAAAE5+fndHl5Gfvb5eUlnZ+fl/oZ5urqip4+fUoHBwdERHRwcEBPnz6lq6urHK0HoH3U0QfeeustGgwGdHp6ShcXF/TWW2/Rt3zLt9D3fu/3Ru0gIvru7/5ueuutt+jRo0f09OlTevLkCT19+pQePXq01ucB6CwuFd2Ef/AsA7B58ni54B0GoD1kyYRhZsGR56g7ZAyAMqEEz7J6/n4zuXfvnn727FndzQBg67i8vKRHjx5REAR0cXER83qV+RkAgD/n5+d0//79WL/6/u//fiIi+smf/Mnob5eXl3R1dUWPHz/2Ps/l5SW99dZb9PM///Pow2ArUUq9rbW+Z3uvt+nGAADKwzR65+fn1Ov16N13340MZZrhtHFwcEBBENCbb75Jp6enXgYzz2cAAP7cv38/Coe4urqiXq9HP/dzP0daa/rYxz5GRM/DK372Z3+Wnjx5EvusHAdsY8HBwQEdHBzQe9/7XvRhAExcLucm/EMYBgDJmMupZunavOEQeTbzYAMQAOmUlQP95OQk6uscRsFZLbjCZtawKPRhsM0QsmEA0F1MA8eGMq/Ba1LMMmIlQdcoo69wCreTk5Oor08mk1hat6zCF/sOwLYDsQxAxzHznxbJh5pHoFYlamHAQRcp4sE1P3tycqKJSI/H47Xz8Tgwn89T+ycmpmDbgVgGoMOU7VluGlgaBl0kz4TWFXY1GAyiTBZ8jBwHdnZ2oqIjtvMAACCWAegsZcQsl+1RqsJDhcphoEvknQDKvsXnWCwWerlcxvr6arWKla/man2z2QyTTgAcQCwD0FFMYXp2dqZXq1VMmKYJ1bJDHao6H4w86AJl9Y+kSanrvfl8Hpt0IvQCgBdALAMAEilbkJZ1PsQsg65Rl0C19Un0LwBeALEMAEil7FCHMs4HzxcAfiT1lSRRbBPR6HdgG4FYBgAk0lTPMgDAjyRBnCZ+zYktPM5gG4FYBgA4aXrMMgDAj7RJqk0082ZA8zOY8IJtI0ks39hktUAAQPO4urqip0+fRqVtDw4OonK6TTgfAMAPWXI+CIK1ctVcLvvy8pKIiD7zmc/QJz/5SXrzzTfpyZMn9PTp0+j9tHMBsE2o52K6mdy7d08/e/as7mYAAAAAjefy8pIePXpEQRDQxcVFbNJqO+Yzn/kMPXnyhH7oh34o9v7V1VUkrJPOBUCXUEq9rbW+Z3uvt+nGAAAAAKBcWASzqD04OIhes/jlv7PHeD6fx4QyEUWC2HUuCGawjSAMAwAAAGg5SeFPMvzi8vKSfuInfoLG4zE9e/YsCsnwPRcA2wjCMAAAAICGcH5+HnmBGQ6NePz4ce7zXl5e0nd+53fSu+++S71ejz73uc8REcFjDMA1SWEY8CwDAAAADcHchMfhFffv3y903oODA7p//z792Z/9Gf3gD/5gFF4BjzEA6UAsA9BBzs/P15ZXLy8v6fz8vKYWAQB8YAH76NEj+vSnP12a5/fy8pLeeecdOj09pYuLi2h8ODg4KOSxBmAbgFgGoINU5Z0qCkQ8AOmUnbZNbv4zU8QBANKBWAagg/h4p+oQrk0V8QA0icvLS7q4uFjzAucFG/YAKIirWkkT/qGCHwDFMMvYSuqqtIfKYAC4QQVMAOqBUMEPgO0jzTtVVWykxOa9JiL6xm/8RlQGA8ACvMAANBCXim7CP3iWAchHFu9UkvfZxtnZ2dp5wjDUZ2dnXu3Y2dnRs9kMnmWwlWTpPwCAzUHwLAOwXfh6p/LERmaJOza919/1Xd9FWmv63Oc+h41GYCtB3D4ALcSlopvwD55lAKqjSGxk1rhj9l7P53N41cDWg7h9AJoHwbMMADApEhuZJbWV9F6/88471nMhzyvYJspODQcAqBaUuwYAZIaXjoMgoIuLC+fGQJnf9eDgYO01ANuIb/8BAGwOlLsGAJRGlgIH2NkPQJxNFwhBISAAigOxDADIRBYB/Pjx4zWPGcIuwDa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      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000\n",
    "X = dist.Uniform(0.0, 5.0).sample(sample_shape=(N,))\n",
    "y = 0.5 * torch.sin(3 * X) + dist.Normal(0.0, 0.2).sample(sample_shape=(N,))\n",
    "plot(plot_observed_data=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the sparse GP is very similar to using the basic GP used above. We just need to add an extra parameter $X_u$ (the inducing points). Let us initialize the inducing points uniformly. During the course of learning, we will also optimize the locations of these inducing points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000\n",
    "X = dist.Uniform(0.0, 5.0).sample(sample_shape=(N,))\n",
    "y = 0.5 * torch.sin(3 * X) + dist.Normal(0.0, 0.2).sample(sample_shape=(N,))\n",
    "plot(plot_observed_data=True)\n",
    "\n",
    "# initialize the inducing inputs\n",
    "Xu = torch.arange(20.0) / 4.0\n",
    "\n",
    "\n",
    "def plot_inducing_points(Xu, ax=None):\n",
    "    for xu in Xu:\n",
    "        g = ax.axvline(xu, color=\"red\", linestyle=\"-.\", alpha=0.5)\n",
    "    ax.legend(\n",
    "        handles=[g],\n",
    "        labels=[\"Inducing Point Locations\"],\n",
    "        bbox_to_anchor=(0.5, 1.15),\n",
    "        loc=\"upper center\",\n",
    "    )\n",
    "\n",
    "\n",
    "plot_inducing_points(Xu, plt.gca())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize the kernel and model\n",
    "pyro.clear_param_store()\n",
    "kernel = gp.kernels.RBF(input_dim=1)\n",
    "# we increase the jitter for better numerical stability\n",
    "sgpr = gp.models.SparseGPRegression(X, y, kernel, Xu=Xu, jitter=1.0e-5)\n",
    "\n",
    "# the way we setup inference is similar to above\n",
    "optimizer = torch.optim.Adam(sgpr.parameters(), lr=0.005)\n",
    "loss_fn = pyro.infer.Trace_ELBO().differentiable_loss\n",
    "losses = []\n",
    "locations = []\n",
    "variances = []\n",
    "lengthscales = []\n",
    "noises = []\n",
    "num_steps = 2000 if not smoke_test else 2\n",
    "for i in range(num_steps):\n",
    "    optimizer.zero_grad()\n",
    "    loss = loss_fn(sgpr.model, sgpr.guide)\n",
    "    locations.append(sgpr.Xu.data.numpy().copy())\n",
    "    variances.append(sgpr.kernel.variance.item())\n",
    "    noises.append(sgpr.noise.item())\n",
    "    lengthscales.append(sgpr.kernel.lengthscale.item())\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    losses.append(loss.item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_loss(losses)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can plot the predictions from the learnt model along with the optimized inducing points locations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(model=sgpr, plot_observed_data=True, plot_predictions=True)\n",
    "plot_inducing_points(sgpr.Xu.data.numpy(), plt.gca())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the model learns a reasonable fit to the data.  We can also see how that the inducing point locations are fairly different from our initialization. We can also view the model learning process via an animation below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "\n",
    "\n",
    "def update(iteration):\n",
    "    pyro.clear_param_store()\n",
    "    ax.cla()\n",
    "    kernel_iter = gp.kernels.RBF(\n",
    "        input_dim=1,\n",
    "        variance=torch.tensor(variances[iteration]),\n",
    "        lengthscale=torch.tensor(lengthscales[iteration]),\n",
    "    )\n",
    "    sgpr_iter = gp.models.SparseGPRegression(\n",
    "        X,\n",
    "        y,\n",
    "        kernel_iter,\n",
    "        Xu=torch.tensor(locations[iteration]),\n",
    "        noise=torch.tensor(noises[iteration]),\n",
    "        jitter=1.0e-5,\n",
    "    )\n",
    "    plot(model=sgpr_iter, plot_observed_data=True, plot_predictions=True, ax=ax)\n",
    "    plot_inducing_points(sgpr_iter.Xu.data.numpy(), ax=ax)\n",
    "    ax.set_title(f\"Iteration: {iteration}, Loss: {losses[iteration]:0.2f}\")\n",
    "    fig.tight_layout()\n",
    "\n",
    "\n",
    "anim = FuncAnimation(fig, update, frames=np.arange(0, num_steps, 30), interval=100)\n",
    "plt.close()\n",
    "anim.save(\"../source/_static/img/svgpr-fit.gif\", fps=60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](../source/_static/img/svgpr-fit.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are three different sparse approximations that are currently implemented in Pyro:\n",
    "\n",
    "- \"DTC\" (Deterministic Training Conditional)\n",
    "\n",
    "- \"FITC\" (Fully Independent Training Conditional)\n",
    "\n",
    "- \"VFE\" (Variational Free Energy) \n",
    "\n",
    "By default, `SparseGPRegression` will use \"VFE\" as the inference method. We can use other methods by passing a different `approx` flag to `SparseGPRegression`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More Sparse GPs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both `GPRegression` and `SparseGPRegression` above are limited to Gaussian likelihoods. We can use other likelihoods with GPs&mdash;for example, we can use the Bernoulli likelihood for classification problems&mdash;but the inference problem becomes more difficult. In this section, we show how to use the `VariationalSparseGP` module, which can handle non-Gaussian likelihoods. So we can compare to what we've done above, we're still going to use a Gaussian likelihood. The point is that the inference that's being done under the hood can support other likelihoods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian Likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# initialize the inducing inputs\n",
    "Xu = torch.arange(10.0) / 2.0\n",
    "\n",
    "# initialize the kernel, likelihood, and model\n",
    "pyro.clear_param_store()\n",
    "kernel = gp.kernels.RBF(input_dim=1)\n",
    "likelihood = gp.likelihoods.Gaussian()\n",
    "# turn on \"whiten\" flag for more stable optimization\n",
    "vsgp = gp.models.VariationalSparseGP(\n",
    "    X, y, kernel, Xu=Xu, likelihood=likelihood, whiten=True\n",
    ")\n",
    "\n",
    "# instead of defining our own training loop, we will\n",
    "# use the built-in support provided by the GP module\n",
    "num_steps = 1500 if not smoke_test else 2\n",
    "losses = gp.util.train(vsgp, num_steps=num_steps)\n",
    "plot_loss(losses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(model=vsgp, plot_observed_data=True, plot_predictions=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GP Classification\n",
    "\n",
    "We will now briefly discuss GP classification for multi-class classification. The two main changes needed to the model specification (in comparison to GP regression) are:\n",
    "\n",
    "$$p(y\\mid f)=\\mathrm{Softmax}(f)$$\n",
    "\n",
    "or $$y \\sim \\mathrm{Categorical(Softmax(f))}$$\n",
    "\n",
    "\n",
    "We will be using the Iris dataset in our example. We will encode the three classes as numbers 0 for setosa, 1 for versicolor, and 2 for virginica. Also, to keep the example simple, we will be considering only two input features (petal length and petal width)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length  sepal_width  petal_length  petal_width species\n",
       "0           5.1          3.5           1.4          0.2  setosa\n",
       "1           4.9          3.0           1.4          0.2  setosa\n",
       "2           4.7          3.2           1.3          0.2  setosa\n",
       "3           4.6          3.1           1.5          0.2  setosa\n",
       "4           5.0          3.6           1.4          0.2  setosa"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = sns.load_dataset(\"iris\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# only take petal length and petal width\n",
    "X = torch.from_numpy(\n",
    "    df[df.columns[2:4]].values.astype(\"float64\"),\n",
    ")\n",
    "df[\"species\"] = df[\"species\"].astype(\"category\")\n",
    "# encode the species as 0, 1, 2\n",
    "y = torch.from_numpy(df[\"species\"].cat.codes.values.copy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Paired, edgecolors=(0, 0, 0))\n",
    "plt.xlabel(\"Feature 1 (Petal length)\")\n",
    "_ = plt.ylabel(\"Feature 2 (Petal width)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "kernel = gp.kernels.RBF(input_dim=2)\n",
    "pyro.clear_param_store()\n",
    "likelihood = gp.likelihoods.MultiClass(num_classes=3)\n",
    "# Important -- we need to add latent_shape argument here to the number of classes we have in the data\n",
    "model = gp.models.VariationalGP(\n",
    "    X,\n",
    "    y,\n",
    "    kernel,\n",
    "    likelihood=likelihood,\n",
    "    whiten=True,\n",
    "    jitter=1e-03,\n",
    "    latent_shape=torch.Size([3]),\n",
    ")\n",
    "num_steps = 1000\n",
    "loss = gp.util.train(model, num_steps=num_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_loss(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 96.00%\n"
     ]
    }
   ],
   "source": [
    "mean, var = model(X)\n",
    "y_hat = model.likelihood(mean, var)\n",
    "\n",
    "print(f\"Accuracy: {(y_hat==y).sum()*100/(len(y)) :0.2f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate the confusion matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay at 0x133782b80>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cm = confusion_matrix(y, y_hat, labels=[0, 1, 2])\n",
    "ConfusionMatrixDisplay(cm).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As before, let us plot our predictions over a 2d grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs = torch.linspace(X[:, 0].min() - 0.5, X[:, 0].max() + 0.5, steps=100)\n",
    "ys = torch.linspace(X[:, 1].min() - 0.5, X[:, 1].max() + 0.5, steps=100)\n",
    "xx, yy = torch.meshgrid(xs, ys, indexing=\"xy\")\n",
    "\n",
    "with torch.no_grad():\n",
    "    mean, var = model(torch.vstack((xx.ravel(), yy.ravel())).t())\n",
    "    Z = model.likelihood(mean, var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_pred_2d(arr, xx, yy, contour=False, ax=None, title=None):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots()\n",
    "    image = ax.imshow(\n",
    "        arr,\n",
    "        interpolation=\"nearest\",\n",
    "        extent=(xx.min(), xx.max(), yy.min(), yy.max()),\n",
    "        aspect=\"equal\",\n",
    "        origin=\"lower\",\n",
    "        cmap=plt.cm.PuOr_r,\n",
    "    )\n",
    "    if contour:\n",
    "        contours = ax.contour(\n",
    "            xx,\n",
    "            yy,\n",
    "            torch.sigmoid(mean).reshape(xx.shape),\n",
    "            levels=[0.5],\n",
    "            linewidths=2,\n",
    "            colors=[\"k\"],\n",
    "        )\n",
    "\n",
    "    divider = make_axes_locatable(ax)\n",
    "    cax = divider.append_axes(\"right\", size=\"5%\", pad=0.1)\n",
    "\n",
    "    ax.get_figure().colorbar(image, cax=cax)\n",
    "    if title:\n",
    "        ax.set_title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(ncols=3, figsize=(16, 4))\n",
    "for cl in [0, 1, 2]:\n",
    "    plot_pred_2d(\n",
    "        mean[cl, :].reshape(xx.shape), xx, yy, ax=ax[cl], title=f\"f (class {cl})\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_class = torch.nn.functional.softmax(mean, dim=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(ncols=3, figsize=(16, 4))\n",
    "for cl in [0, 1, 2]:\n",
    "    plot_pred_2d(\n",
    "        p_class[cl, :].reshape(xx.shape), xx, yy, ax=ax[cl], title=f\" p(class {cl})\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ankU0/RNvhmEYPYYgpqam255GNJ0TFimxA/7ddl4NCn8m1ifnqDHmLkj34akp4Wd4EF+KIdr3HLQnqpygNW1ZVc3z0XinhYhVBZqx2qgNElOL04sftUVrwsJNJJiyAPlUUr4FdL7qp75kfD6BFFq0Yt1JfXYRbUS7JjW4RjCG+o2t8+2ycFNQ3S72O8y1LaTYPEylZQyDnGpUDUXycgBnArhfRI4b8vl6AJ8E8E/FW7Mi8hdV/XbuZGEYhjHWEGCzaqgrMAiS3hhoE11/qDVh4Uv34RIuqxqX70hbYEk7lzk0aqjytT7jvCbPlG+MMrEZXrXPwbdzjg0uDHlVadvFzDUXrWeV5qRop4xJh5hu8GQhIl8uyknUip0sDMMwRgg5hanFWcJiGck7nNczIjIT2UdU/SGgI8LCt7suE3ua0ERXh+IINHUkNMby8unDlyxRc38pxlwXTQxEqH3sCU1zwtE6MuSQa3OIbRO6xphw8tVQD2Sm+1DVHyrTuXQfLuWFWCMgYgVKKI5gPtVqKJ/gKL/vS2+iIZRe3UWzeGsET0iY+mqix6qk6qyApyUnjbo2Y65hDGNg4G7PG8otXici15P8IMllIvJA6LrK4kckV5K8keQ2kltJnj+kDUl+gOTdJL9Bcm3abRiGYYw5RVBe6r/84XloUacI2vpDgO5ksRvAG0VkM8mnAriT5A0i8m2nzUswOMasAnASgEuK/724Bm5NPW0gvm5F7Cmj3JeLNjZD06cvjsA3huY+QnWscyLGw1H06aonF62B2yW35kXsNSkJHHPGthPKeNNkUB7JqwCsx8C2sR3AOwAsBtLrDwG6ehY7AOwofv4lyW0AVgBwhcVLAWwsBryV5FKSy4tro9Cm+3CJXchDFbByhIJvjNw+NYtn2HMsLu12aAHULP6a+I9QP7ECwkW72M+LY/HYYTTxMKF+feObgOg/2mJYw2g6zkJEXl7xeVL9oSibReGOtQbAbaWPVgC413m9vXgvWlgYhmGMO5zuX7oPdfEjkksAfAnAu0VktvTZZwBcWFTVA8kvAHiTiNxZarcBwAYAWLly5fO+993vBMfUGld9bUKxDqMkpIbS1MDw3Yc2xYdmPO1JKKVmR19JUT3Z6cAAwsWPnrdqmdz2/jOS+158xsbuFj8iuRjANQA+UhYUBdsBrHReH46B/+48Cl/gGWBQKW/uDytUmc1Fo3sftZeNRmUSWnw1Noi8ok/+dr5sq9ra4znqIu0cXep0ZY29ftRuyiZ02qep74Nkq95QqWi8oQjgMgDbROS9nmbXAXhl4RV1MoAHU+wVhmEY4w8BTqf/a2vWVWooks8HcDOAbwLYW7z9VgBHAAPreiFQLgZwGoBHALxaRO4Y0t0+nrd2rdxyyyYAabWrc9RKocSFmhrVGq8ll9DuXFv7uorcuhMpu/MmPKPK5MVv+A2POXVLcuuH14mdRrpJSA11wjHPlNsvOTu57+lTP9CKGkpts6ibA7lUjsYgKG8UdgZtoZ5YW0jsAhbqN9ft16UpAeEj1sOnKXVRU+RGbde5qMeqtyaNLgjQoLD4zUPl9plXJvc9/a/e012bhWEYhlEXbFWdlEprJ4vDlkzJhtUDI0/KCUKzc9bs1EOqkdidfoqaLFY1o607oVHH+HZg2pNXbJ4q7e68rhPEKE4iKXEWPizP1PgQPlkcJrdfviG57+l175pcNZQPbfRwjn5f656bYo+YQ+s666JRx6Xch6+Nj1C/vsW4TltGm6onDaGF2yK1+01O4F1QWBy7Qm6/4tzkeU2f/F9NDWUYhjH+ELAa3PloSn0C/jTfdfbrxnL4doYpWWc1pxeNak2b8ymnbnaKB1OdxZa6bsjWzi8lf5UPO6XoyTkdxLZXQ4LT/YuzaE0N5XOddQkm4HPIWQxzPa5yvZZ8aL23cuhbBHYf5hsrCGyBH0+CaqjnHClf++h/Se57avW5poYyDMOYCKb6t/S2NuNtd92zb6fo250vqNJWU2oMl9zArZQCS77rY1OR13niSDE4u4xCXdRUjEidxKqbUtRTpoYaDTkqrCCcAqabyzrbFP0Tb4ZhGL2GQA9tFq0JC7f4kW8XrbUB5MRZpBifNaTsRDRJ/rTPqq77WNhv87t4zXzbPE3kFliaZPr0TJo0cPfRG6pzcRa5qbJj24RoKhVHTgxEblpxH3WqtzSBe11VIzWFqY4mi6CB+7ePlq998n8m9z31G//GDNyGYRhjD00NlYymIA8wf8dbZ9S2jzpdYTVoaom7pLj9+vr11bPQprNw8Rmi54/d7mkiVjWXm5XXV1sl18Bt9BHLDRWFL+usiza1d1NV8EYxRl1xGinZc1NsGZprcrPydjWGoi1CAtsERzcJqqGee4zcfv2lyX1Pr3xhK2ooTfGjy0neT/Jbns/Xk3yQ5Jbi39vrn6ZhGMaYQAJTi9P/tTVtRfGjFwDYBWCjiBw35PP1AC4QkTNjBtYkEkwhtkiRtviRj5RaHLEnKdtpjy911rawU0Z3CJ4sjv9Nue2zlyf3vWjFum4auEXkyySPGsFcFpCrWvExv838Rd0X+Kfpy9XDa+tYx+a40mR6LdPFFCF9SN2RQl25pVKy2Rp9ga2eEFKpy8B9CsmvA/gxBqeMrTX1axiGMVYICZlQYbEZwJEisovk6QCuBbBqWEOSGwBsAIBD9gfOOmFh0Euuh4+LxstKG5QX20a7c9bcr8aLKDceQqsaq+sUME6nCZe6YkZyTw92+miHub/nndgUaNVPb6hsYSEiDzk/X0/ygySXicgDQ9rOAJgBBjaL2VvCNgutd1CdmV81aqHciPPcfFKx4/ltNHH3p6UpFdO4qK7qDNDTqLEs++3omPu9XLcutLZN6MmC5KEA7hMRIXkiBh5W4x+SaxiGkQL7abPQeENdBWA9gGUA7gPwDgCLAUBELiV5HoDXAtgN4FEAbxCRr1QNnFtW1aXNeIjclCB1pf7QMoo4C6NZYut5T9qpYRT3XpWRNuQN9bw1z5Vbv3hd8tj7Pf3XrQb3qGiqYFFKv3XV/C63j00lbm67/aGuBXAS7CKNpRmvICwsjpev3nR9ct/7Lz28m0F5hmEYRo00HJSnCKQmyQ+QvJvkN0iu1Uy7EynKm1IdpdCUuslFs8PxeW+53lDa8TQGTl922KaYtKyzOWh37Zqdfp3PuqunCRdN1mMN5eeW66QgzXpDXQHgYgAbPZ+/BAOP1VUATgJwSfF/kLFWQ43CllEnOYJKS12eWEaz1JlUMCXwL5YuqaTaUj25BNVQa9fIVzZ9KbnvAw46pFINVQRSf9qTdeNDAG4SkauK198FsF5EdoT67ETWWcMwjImh/aC8FQDudV5vL97rvrCo0zDs0ofThEtsgF/KKUOjbgrluLJTx2jQqouaCAIE2j8dVBE6PWhqtbd5fyKEyNBDh5ZlJO9wXs8UMWxahg1eqWLqhLAwDMOYHAR792ap/x/I9IbaDmCl8/pwDFI1BemEsEhxXx11YSKXplxvNWP4xkspUuR3lx2eELF8jZ0y8sk19GsSS3Zpp13XmCFbhK/fLp2WMoVFLtcBOI/k1RgYth+sslcALQqLY9c8C7fcMvglzk1bMQp1k6+KnUudwXOxMRehhcaXW2o2YeE3AVEvTXmCaQRECrHG8lGot7qkQpuby6cC6T5EgL0NOha5gdQkt6MUSA3gegCnA7gbwCMAXq3ptxMnC8MwjEli757mhIWIvLzicwFwbmy/rQmLbXfdU7njDqf7OHVou5za3CnX+6hTPZWS/db9zHcaSDklWHzEfFLUf5q+tO6ysePl7rp9J3pfjfGmdvkp6qymXGrnaTaKuez43uPe9iLAnr21DT8yOn2yqDOLa+61sanEQ4wi8M9HnTYHs1/Uu6g3FTCXsrBqrskNeMuxX6QIoToFxLzvKmEubcW35dBpYWEYhjFuSL43VCuMdQR3n8k9TdSVzTZ0YrDkg91Fc6pJ2Z1rVDmhcr+a3X3siaN86tfMq2kjeCiC+/jj18hnP39Tct8rli/tZg1uox3qDMSLLaSkFRAmFNrHJxR8C6NPcGhzH71Z0cZ932fLCBErIEICaJg9oQtID20WlVlnm8pgaBiGMYmIDOIsUv+1heZkcQUayGA4LowiQM83nou2wJKG0E7UThPdIvYEkWv4bjuobw6tsTrWqF1XjY9QnAUA7OmhzaJSWIjIl4sMhj5eCmBj4bt7K8mlJJdrIgJziF2km1rURx1J3tTcTQh0i5T8XD4BkesyOmoBoRGAo86Yq7WLzF0fdJ2FTKw3lDqDIckNADYAwGI8pYahDcMweoY0G5TXFHUIC3UGwyIz4gww8Iaq6jgUMBe7wx71CSA3k65Lbg0K3wnCd402lYqdRprDZ1TW4n6HboqXXEax04/N7aQ1zmv68lFnjIZgTNVQCpIyGGqoM135qKkzOWJKFbu8dOfD80eVrzG6S2yAnza/ks+7SCs4YgWMpn2KvSXl+jrpoRaqFmGRlMHQMAxjIhFgz+7++c5WCoumMhjWSZ2nia6cUnzzKO/0RzkPY3zR7q5za7VrVElumzq9tzS4J6fQ737OaUREsKeHyaFai+A+bMmUbFi9PwC/t4Y29XidqcH7ijYhouZZ5S4Ihp6m6lnkto9dpJtSQ42Cutxl3etDEdzPec7xctVVn4seZ47jjz/MIrgNwzDGHempGspyQ40JuSk6LOZiMtCeGGJPKb5rQzv1plKGx87Fp8EInbCrTiChk8VvHftc2XjlZ4LXh/idk46wk4VhGMa4I2i2Ul5TmLDoKLFZYyfJPmOkk5tIsE47Q1OnCRfNfFOy1GbFb/RUDWXCIpMUg7yGrnp4WaW8yWO+88OT78fmnyp/1hSx6i1f+1BwqhsoOayC505s8o4nIiYsDMMwjGpkQiO4J5o6TxM+UgoZdaUwkRnO2yc3/UXO97awNnx9hZjmWHBPChWa+74bu+Q7ZYT+voYZwtcFss6KoJdxFiYsxoSQesl3nE4RQu71KTmLjNGQq+6pK/V5qOBQbLoP37Xlftzf0VmPCk1ToClks9Co4/yYGsowDMOoYK74Ud8wYdED6iyl6u60NEkFcxmFx4uxkNjdbsiAW9spI/CZJsnffBXR0OYA5v8ua2JBfCqllNOZpp5FX72hehWU18SCptX1d53yoqyxpaSooXzUaZto0+NqUm0s2hQdKddr0KT8yd14aASE5toywwTa3diER2Tn0KC8VUc/R973nr+rnrCHM8/6bQvKMwzDGHvEvKEap4ldfx9OEpoTgLZIUWyAX25NkZT0Im3Gb3TxNLHQo6h6jnWeznKSCpbnHr2LzwwO9F8T58Wo/Q7m7m9mS6isKrC7h2oolbAgeRqA9wOYBvBhEbmo9Pl6AJ8E8E/FW7Mi8hf1TXOySamU51vwc1VPGkHQlQU3tGD2Sd2UMr9cAZElFAKLcl3R4HVGlWs8BLUqsLm+qoLydj+xJ3aaraOpZzEN4G8AvAiDqnhfI3mdiHy71PRmETmzgTkahmGMDwLs3du/k0WlgZvkKQDeKSIvLl6/BQBE5EKnzXoAF8QIC8s62yw5zgC5J4uc9kY38H1vmpgdl7rqQ/SNUNbZZx11rPzV269I7vtP/uzkzhq4VwC413m9HYPyqWVOIfl1DOpvXyAiW1Mm1FSupa7SlMtqTl+ha2NtE7ECRXuNkUaKLcOXG8qnmklZ4GNre+d6SdVZ8ChWXTUKNVQTpgONsBgmHcvHkc0AjhSRXSRPB3AtgFULOiI3ANgAAIvxFMXQhmEY40eTQXlNmQ40wmI7gJXO68MxOD3sQ0Qecn6+nuQHSS4TkQdK7WYAzAADNdSwwSbhNOHSlDeW5gSQG1uR4wE1P++OZa9tg9ApIzawLVdd5Cs05OtXM78ysUb/kFeXG7QYe7IRAXbvbvRkcSKAu0XkHgAgeTWAlwIoC4soNMLiawBWkfx1AD8CcDaAf+c2IHkogPtEREieCGAKgK0AhmEYJUQEe/LUUMtI3uG8nik24nM0YjqoFBYispvkeQA+j4H+63IR2UrynOLzSwH8IYDXktwN4FEAZ0tboeETSq6e37dTC+3G6jKcp5T0HEdynQFi4yF8CffKaE5+2my2dZ1GclJxAGUNhkeb4bQvP4Pck1SmN9QDFQbu2kwHLqo4CxG5HsD1pfcudX6+GMDFmr7qYtIM4XPkBs/5GFbABVi4iLjj12Wcn1ThANTrLaZ5jm4bfwGfvHgD7QbDXYB9cRpZFelK5BRFCmVYju1XRJpWQ9VmOnDpVQS3YRhG3xmBN1QjpoNeJRI09KS4rMb2ozGcp+yWc64fl7iOLpWv1TxTjRG83FesUbspfPEiobKqVYQSCa48bJW8/jXvj53mPi545xmVcRaFaul9eNJ08G7XdFCYFl4LYM508AYR+Uqoz9ZOFksPeghnrR78skySGqkNNELB94cbUk80tRjHCp6LArrlUVOXsNKrcur5DsKV8tK9iLTtclKJh9KgawIHXbVXShGnYVTnhmo2zqIJ04GpoQzDMEZIX3NDmRrKWEDIcF2Xumlc1EVtkxPfotp1BxhF/IXPeBwaI8co7tNyxD6fdeuejzs3bx6qhlpx6NFyziv/Oqo/l7e/5w86m+7D6BApHkiaRUTzvrZfX1+jUGFpxu4bocUwJQX8vn6U42v60qTr0DK/PnZ8ShHffH1z0eTBCjG8+NE93vaDk0X/EgmasDAMwxghIsCeX/VPDWXCogeM4jShbd+n3XqdgW1tkjIPjTOAtlSor961RkWkpU4PKE2AaWxckHZ+muJHEMHePXayaJRJCsTLDXgbdc4pX5scNYkWjRohxUOnzrk0Rawrap2eSpoAtPK1mgC2OosRaQSE21dd2QvCxY+APb8yYWEYhmGEEMFuU0M1yzieJppK35Ezdog+eUC1cUqoMzgxZ7zZeWPHewdpPIpi80+V5xsb06A1PmvqXsxL5aEqD1ueS/jeg3EWAlNDGfF0USho28e6bWoX0thFdhQLcVPX1ylQYq/PVc1p9PjlOfkWctczS6c68s9Po5pzx/MFdQYjuHNsLCJm4DYMwzDCmM3C6Cwaw2CK+sSnNtMYuEP9dt3Lqk7qvNdYFZE2eM630/ftwtXqLcXuPNepxXd68ZWKHUleqnH2hlLUc2Xx+ekAHgHwKhHZXPNcR0JTNbG7Qp16fN8fcqxqRRsl7mujoQ91vrUVDWPn7tPb+xb+8me+qnCaRHshNZQPX7p8jX2mPEcfsdXtyu2rvM0+tc6fnUIE42ngVtZzfQkGhTNWYVCR6RIMr8xkGIYx0YhIL9VQlbmhSJ4C4J0i8uLi9VsAQEQudNp8CMBNInJV8fq7ANaLyA5fvym5ocZ915+DVl2Ucn1Ov5pstilp0GPn18ZJQuOznxIDUVfgYJ21q1PmFPv7oy0y5DvlaOJQtIGGVardmS2P48e79g7NDbVsyRFy5vEXeOdfxZVfOb+zuaE09VyHtVkBwCssDMMwJhEZY28oTT1XTRuQ3ABgAwAsxlMUQ89n/k6oWkc6jqeP3LgMzfUpu3CN66yr+64zbiElWeEo0nroEtfF7dpD/WqIHbs8fuwpI2SUjk4RoiywNOvZ9Wui2n3JFct/X7E2D5eBzaJ/aiiNsKis56psAxGZATADDNRQUTOFzhtiHAWES721tuPbuwuw7w9Gk802RW1WZ8Bbm3mf6oyH0BYEGtYmhM/I7FtMU1J7a9RgGhVRrgOAZh6+/FhAQkp2EciYekNV1nMFcB2A80hejYGK6sGQvcIwDGNSEcH4Fj9S1HMlBiX6TsPAdfbVInJHqE8rftQsOVHbIWJdWVPcK3NODSl1k0dh/K5TlVNXtLw2MV9TpzBNYj8f2gyyOVH0OQ4AoeJHTztghaw//BxV38O49h/f3lkDt6aeqwA4t96pGTnkqJtyffx9evFZpRCoq3a1trhPjv1C+3xyssDqVTnVwjilXnlOWpeUdpoa2rn34aKJPdHGAs31teN7odxQApHxVEMZhmEYtSHYs+eJticRTWs1uA9bMiUbVu8PYDyzyY6Cpjy/Umpwa/rSUld8RFNxFqOIEUnJCOu7vik10qjH0MZZ5Kj5tB5aOXEWh+x3qKx75p9WztHHZ7f/dXfVUE2w8+GDMXvLQptFnQvVuJP7DDRutFrvmToD5roefNeUgHBJWXx9+Y585AYE6uah+/3RpBLXBHgCmOdiqxUww/oN3+uT/Q7b7IaKHwHA3r2mhjIMwzACiJgaKgrzhuonmiyguUn+fOON2itHY4AtU9ccmyo766I9qeeUqg09K81pIuU70Ki1facM34lFq/aam1dIDXXw4n8hJyz9o8o5+rjxgQ9OlhrKZZJqazdFyP3U1y6lTWxgZJ3Fi5pSN9WpLsrJkusugBo1krYvXaU8//eqSX2uSWO+cF7xbqrDCLkWaxZ83z2534G24t9cu6oa3KaGMgzDMCowNVQU46KGGsWpqM2TV53ZbDU70dCYbWeRHTaPMk3U4NbmhopVEYXmFxvcmKKqqqvQkNZrKUWl5Ruj6gQZCspbMr1MnnvgGZVj+vjqro2Tq4aqk1EvrH0Yo+rIXAeaxTAlRblmjKb0+ylV/lKCxepCo29324Tuw23nS8yXi67WdrXNKrTY+6rgaYSp+/cRKrDktpsbIxSUB/QzKG+q7QkYhmFMEnPeUKn/NJA8jeR3Sd5NckEyAw74QPH5N0iurepz7E4WfTOQxxYHSomt8GUQzSXXWN7EPFy0apb5fcWdfppSEYXQ9BVrPC63iY1P0MZ4aILh5tXNTnhWmuJHvmeimVP5dbyhvlmbRVPVTc1mMQFo3BJT6mG41FUrO9RvrP2jzjrWfUAjRLQpzXOEW51V83Jdp7V2smHjucTaXkKuswfyaXLM9Hpvf1Vs2XNt0GbRVHXTsTtZGIZhdJvGvaEaqW7a2smC5E8B/LCh7pcBeKChvpvC5jwa+jhnoJ/znuQ5Hykizxj2AcnPFeOkcgCAx5zXM0Vhubn+/wjAi0XkPxSvXwHgRBF5ndPmMwAuFJFNxesvAHiTiNzpG7S1k4XvQdYByTvacC3LweY8Gvo4Z6Cf87Y5D0dETmuyf9RY3dTFvKEMwzDGi33VTUnuh0F10+tKba4D8MrCK+pkKKqbms3CMAxjjBCR3STPA/B5PFnddKtb3RSDYnanA7gbRXXTqn7HVVjMVDfpHDbn0dDHOQP9nLfNuSWaqG7amoHbMAzD6A9mszAMwzAqGSthQfJykveT/Fbbc9FCciXJG0luI7mV5Pltz6kKkgeQvJ3k14s5v6vtOWkhOU3yLpKfbnsuGkj+gOQ3SW4heUfb89FAcinJj5P8TvF7fUrbc6qC5DHFM5779xDJ17c9ry4xVmooki8AsAvARhE5ru35aCC5HMByEdlM8qkA7gTwslJofqcgSQAHicgukosBbAJwvojc2vLUKiH5BgAnADhYRM5sez5VkPwBgBNEpDfxCiSvBHCziHy48MY5UER2tjwtNUW6jB8BOElEmooF6x1jdbIQkS8D+Hnb84hBRHaIyObi518C2IZBJGVnkQG7ipeLi3+d33WQPBzAGQA+3PZcxhWSBwN4AYDLAEBEftUnQVFwKoB/NEExn7ESFn2H5FEA1gC4reWpVFKoc7YAuB/ADSLS+TkDeB+ANwHoU35oAfAPJO8kuaHtySh4FoCfAvjbQt33YZIHtT2pSM4GcFXbk+gaJiw6AsklAK4B8HoReajt+VQhIntEZDUGkZ8nkuy02o/kmQDuD6Uz6CjrRGQtBllCzy1UrV1mEYC1AC4RkTUAHgawIEV2VynUZr8P4O/bnkvXMGHRAQq9/zUAPiIis23PJ4ZCxXATgKZTGOSyDsDvFzaAqwG8kOT/bXdK1YjIj4v/7wfwCQAntjujSrYD2O6cND+OgfDoCy8BsFlE7mt7Il3DhEXLFMbiywBsE5H3tj0fDSSfQXJp8fNTAPwugO+0OqkKROQtInK4iByFgZrhiyLy71ueVhCSBxVODyhUOf8aQKc9/UTkJwDuJXlM8dapADrrrDGEl8NUUEMZqwhuklcBWA9gGcntAN4hIpe1O6tK1gF4BYBvFjYAAHhrEYHZVZYDuLLwGpkC8DER6YUras94JoBPDPYTWATgoyLyuXanpOJ1AD5SqHTugSKVRBcgeSAGBYNe0/ZcushYuc4ahmEYzWBqKMMwDKMSExaGYRhGJSYsDMMwjEpMWBiGYRiVmLAwDMMwKjFhYRiGYVRiwsIwDMOoxISFYRiGUcn/B3gnA7Xerc58AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pred_2d(Z.reshape(xx.shape), xx, yy, title=\"Prediction\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see our model doing a good job in classifying the IRIS data based on the two features. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Combining Kernels\n",
    "\n",
    "We now look into combining different kernels. We will create a simple data set containing a linear trend and some periodicity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAD4CAYAAADxeG0DAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAW/ElEQVR4nO3dfYwdZ3XH8d/x5ra5Li3rKoaSTVJbCLlNSetIVymSpTaYF4cXkcA/LgiE1KrpH41ErOJ2A1UbqkpYDdT5o4jWVFGpgsBIBENx2xBwK1SraVljkxdBSkRDyDoli8iqUK9g45z+sTvOeDyvd557Z+bO9yNF9l7fnTsLyvGTM7/nPObuAgB015ambwAAUA+FHAA6jkIOAB1HIQeAjqOQA0DHXdbEh15xxRW+Y8eOJj4aADrr1KlT33f37cnXGynkO3bs0NLSUhMfDQCdZWbfSXud1goAdByFHAA6jkIOAB1HIQeAjqOQA0DHlS7kZnaPmT1jZo/EXrvTzJbN7MzmP2+czG0CQLccO72sPYdOaOfice05dELHTi9P7LOs7PRDM/sNST+S9Pfu/srN1+6U9CN3/1CVDx2NRk78EMCsOnZ6WXfc97DW1s9feG2wxfSiyy/T6rl1XTk/1MF9u3TL9QuVrmtmp9x9lHy99Irc3b8i6QeVPhUAeuiu+x+7qIhL0vrzrmfPrcslLa+u6Y77Hg62Sg/RI7/NzB7abL1sy3qTmd1qZktmtrSyshLgYwGgnc6urhW+Z239vO66/7Egn1e3kH9U0ssl7Zb0tKQPZ73R3Y+4+8jdR9u3X7LDFABmxpXzw1LvK1Pwy6hVyN39e+5+3t2fl/QxSTcEuSsA6LCD+3ZpOJgrfF/Zgl+kViE3s5fFvnyrpEey3gsAfXHL9Qv64Nuu08L8UCZpfjjQYM4ues9wMKeD+3YF+bzSQ7PM7JOSbpR0hZk9JelPJd1oZrsluaQnJP1ekLsCgA46dnpZd93/mM6url2STMn7s7pKxw9DIn4IYNakRQ6Hgzl98G3XhSvYdeOHAIBsaZHDkMmUPBRyAAggK4ESKpmSh0IOAAFkJVBCJVPyUMgBIIC0yGHIZEqeRo56A4BZEz3QnFQyJQ+FHABqmGSssCwKOYDeG7cYJyOH0TAsSVMt5vTIAfRaVIyXV9cqTyZsMnIYx4ocQC9Fq/DllHhgVIyLVtVNRg7jWJED6J34KjxLmWLcZOQwjkIOoHfSWiJJZYpxk5HDOAo5gN4pWm2bNnrlRWdtJqccLswPg85WKYseOYDeuXJ+mNlWMW2Mc5XKpVBuuX5h6oU7iRU5gN6ITrZfXl2TJf5sOJjTtq0DJefBNpFCqYpCDqAXkg84XbpQzKOWyOq59dTvTbZior8Qdi4eL2y/TAOtFQC9kPaA07VRxE8u7r3wnrSWi0vac+jEhYeYbdgEFMeKHEAvlMl85521GRXsD/zDo63YBBRHIQfQC2Uy3/EUSpq19fN6tmT7ZZoo5AB6oWzm+5brF3Ryce8lD0OLTHsTUByFHEAvVM18VynMTWwCiuNhJ4DeqJL5Prhv1yWHKadZaGh0bRyFHECrNTXvO35QRNbmoXjipUkUcgCtE59MWHWnZda1xvmLIFrBJ+eOS823U+LokQNolbSNO3FVon51Zo3HtWWmShZzT/7PNHmj0ciXlpam/rkA2i/aQl+kTG8661ptaYlUZWan3H2UfJ0VOYBWKZvHLrO6bsvBD5NGIQfQKlVif0VtlrYc/DBpFHIArZK2cSdvc07e6rotBz9MGoUcQKukPVg8vH935rb5vNV12x9ShkL8EEArlIkJJiOA8ZN8sh58tuHgh0mjkANoXDKnnZYXT27QycuXN7WJqCm0VgA0Lm1WeNqDzGig1cL8MDNfHio73iUUcgCNqxoTzHp9eXVNtx8907p54ZNGIQfQuKoxwXHig7OWHY+jkANoXNWYYN5JPllmLTsex8NOALWEeLAYf5BZ5jrJ9xcNGpnF7Hgcs1YAjC1tKmCUJpnmnO68+SxtmBceSu1ZK2Z2j5k9Y2aPxF77eTN7wMy+tfnrtlA3DKD9sk6ml6abFslqzdy9f7dOLu6diSKep0qP/O8k3ZR4bVHSl939FZK+vPk1gBl37PRyqSmFRWmR6Do7F49rz6ETYxf9vuzgzFK6R+7uXzGzHYmXb5Z04+bvPy7pXyX9UYgbA9BOae2UPFlpkTKbgKroww7OLHVTKy9196clafPXl2S90cxuNbMlM1taWVmp+bEAmpLWTsmTlRYpuwkIxaYWP3T3I+4+cvfR9u3bp/WxAALLy2MnpxTmpUX6Mit8GuoW8u+Z2cskafPXZ+rfEoA2y1phx6cUmqT54UCXD7bowNEzqf3vvswKn4a6hfzzkt69+ft3S/pczesBaLm8zTvRLJTD+3frx889r2fPrWfOO+nLrPBpqBI//KSkf5e0y8yeMrPfkXRI0uvM7FuSXrf5NYAZViYhUqb/3fekSUhsCAIQ3M7F45m7LeeHA5lJq+fWezFiNiQOXwYwNXl97tW19dyWC6qjkAMopcrmnSpDrYgc1sfQLGCGhTopp+rmneRpPkWIHNbDihyYUSFPyhln8078NJ8iRA7roZADMyrkzsk6m3eK2ixEDuujkAMzKu84tKoDqups3knGDOeHA23bOiByGBA9cmBGXTk/zOxPVx1QdXDfrksGZVVZSfd5oNU0sCIHZkx8xGxy9klclTYLm3fajRU5MEOS6RLXCyf2pKmSFmFV3V6syIEZknViz5ylr81dyu2Xhzr4AZPFihyYIVkr7PPuGg7mUueIZ/XLQx/8gMlhRQ7MkLwRs1GPO01av5yDH7qDQg7MkDIjZrMegCZX8xz80B0UcmCGlEmXZK3ak/1yDn7oDsbYAj1TdHhylHKZHw70fz95TuvnX6gRw8EcscMGZY2x5WEn0DNFA62isr26tq7BFtO2rQNmh7cchRyYAVWnHEaZ8LwDICRp/XnX1p+6TKf/5PXhbxrBUMiBBoUYM1snJpi3jT/Cw83242En0JC0MbMHjp7Rjoqbb+rEBMscAMHDzfZjRQ40JGsXplRtVV0nJpjslye38zNithtYkQMNKSq0ZVfVdWOCUb78iUNv0uH9uxmM1UGsyIGGhOpP1x0xG8dgrG5iRQ40pEx/umiolcSIWbAiBxpT1J+OlOmXs5LuNwo5MEVpccOTi3sv+rO0dkvUL6dYIw2FHJiSorx30SadZL88RAYds4EeOTAlZfPeZVIoaRn0O+57mIMfeopCDkxJ2bx33ijaCLPCEUdrBZiSrLhhcgUefwh6dnVNLx4OZCYdOHpGd37+UZlJz55bT/0MttP3EytyYErKrLQj0Sadw/t368fPPa9nz63LtTGRMKuIS2yn7ytW5MCUJFfaZR5QprVQsrCdvr8o5MAUVc17l22VLJBa6TUKOZAhHu+L+tTTPmChzDb+hfnhhSw6+okeOZAiGe+LetPjRP2OnV7WnkMntLPieFqpeBs/7RRIFHIgVVFvumzUr27eOzlHZX440LatA2aq4CK0VoAUZXrTZd6Tl/cuW4CZo4IiQVbkZvaEmT1sZmfMbCnENYEmlYnxlZlMWOfQB6CskK2VV7v7bncfBbwm0IgyI2al4lZJ3UMfgDLokQMpsnrTafL65VU2AQHjCtUjd0lfNDOX9DfufiT5BjO7VdKtknTNNdcE+lhgctJ602UnE8avIVXbBARUFaqQ73H3s2b2EkkPmNk33f0r8TdsFvcjkjQajdL+XQBar+y8lDgeVmLSgrRW3P3s5q/PSPqspBtCXBeYtqLMd1qrxLTRK4+/v052HKiq9orczH5G0hZ3/+Hm718v6c9q3xkwZUUHP8R/TTueLXr/0nd+oM+cWs69DhBSiBX5SyX9m5l9XdJ/Sjru7v8c4LrAVJWd8R1NJlyYH17SL19bP697H3ySWeGYqtorcnf/tqRfC3AvQKOqZr6rZsHJjmNS2NmJzgt1dmXVB5llBlqVuQ5QFzlydFrIsyurZr7Lbhoqug5QF4UcnRby7MrkJqCioVTx9+dhuBUmzdynH+kejUa+tMRIFtSXtUFH2ogFTmsDTjLxIm2swingCMnMTqWNQaFHjk6K+uJ5y5B4q0XKjv6F6LGzgxNNYkWOzklb/RbJOkWHlTS6JGtFTo8cnVPlQOJIVvQvZI8daAqFHJ2TVZSjB5RpsqJ/zAvHLKCQo3Pyct1lZ6GUuRbQFRRydE5e3jsZCUybhRIv5swLxyygkKNzivLeRbNQ4v3vqtlxoI2IH6IzqsYE8/rfobb1A21AIUcnlBkxm5Q1C+XFw0HlawFtRmsFnTBOTDDrwefq2jqRQ8wUVuTohHFignmHQFS9FtBmrMgxcSGOPRs3Jpj34LPqtYC2opBjokKNma0bEyxabRM5RJdRyDFRWb3t24+eqbQ6rxsTzFttEzlE19Ejx0RE8b68E3SqpkVuuX5h7GJ7cN8uhmNhZlHIEVyV6YRRWmSSI2YlxsxitlHIEVzV6YRZ/etxsuN56qzogTajR47gqsb4XErtlzNiFiiHQo7gsh4szg8HmYcVp6VZGDELlEMhR3BZUcE73/IruYcVJ1fbjJgFyqGQI7i8qGC0Qccyvje+2mbELFAODzsxEUUPFrMGWsVX2yRNgHIo5GhEWq47Osln9we+KDNp9dw6xRsogUKORuQNtFpdW7/wPkbMAsXokSOYqsOxyg60InII5GNF3nOhdk7W2bxTJk5I5BDIxoq8x9ImEx44ekY7xhg3W2fzTpk4IZFDIBuFvMfSim/eifN56mzeSYsZxhE5BPJRyHusqMhW6U3X2byTzJ3PDwfatnXAqfZASfTIeywryx1XtjedNSa27EqagVbA+FiR91hRS0Mq35uue/ADgPGZe9FJhuGNRiNfWlqa+udiQzyp8uLhQGbSs+fWLzmcOPp6gU05QCuY2Sl3HyVfp7XSM8mY4OrauoaDOd29f7ek9A06eVHCUPFFAOML0loxs5vM7DEze9zMFkNcE5ORFxPM26CT9uAz1MHKAOqpXcjNbE7SRyS9QdK1kt5uZtfWvS4mo0xMsGyUkIMfgHYIsSK/QdLj7v5td/+JpE9JujnAdTEBZWKCZaOEHPwAtEOIQr4g6buxr5/afO0iZnarmS2Z2dLKykqAj8U4ysz4TntPNJlwz6ET+uNjD2vPoROZ81HYhQlMV4iHnWlnBFzy77i7H5F0RNpIrQT4XIyhzIzvvMmEy6truvfBJzOvzy5MYPpCFPKnJF0d+/oqSWcDXBcTUmbzTfSePYdOFG4aihBTBJoRopB/VdIrzGynpGVJvyXpHQGuixYo2+82SScX9072ZgCkql3I3f05M7tN0v2S5iTd4+6P1r4zSAo7Znac65TZxh+9D0Az2NnZYsnNO9J4uy3TrjMczJXaQp/2vUllrwWgnqydncxaabFQY2br5L3TZqi881XXMFMFaBG26LdY2TGz457AU7b/zWRCoN1YkbdYmb5zlO3OW5nXmRUOoP0o5C1WZsysVNxmKbMJCEB3UchbLN6fltJ3XkXyet7MCgdmGz3yFsqKCkavZ8UBkz1vRswC/UAhb5lk3C85Czxvt2W85110HQCzg9ZKy5SJChYNtYpW4oyYBfqBFXnLlIkKFg21ytvAw4hZYPawIm+ZslHBotN8ql4fQHdRyFumalSwygqbyCEwm2itBBIqIVJmXnhc2aFWjJgFZhdDswKoM5RqEp+dZJL++9CbJnofACaPoVkT1GRCJLlpKA19cWC2UchrOHZ6OfcEnTJzUJLX2rl4vPT3RKIHn3fv381WfKCH6JGPqUxLQyq3ESfU5p2q/XUAs4FCPqa0dkqWonGzea2ZqkWYkbNA/9BaGVPVjTV57687LxxAv1HIx5T1AHHO0mcU5j1wZF44gDoo5GPK2rjz9l+/uvIDR+aFA6iDQj6mrBnff37LdRe9Pj8c6PLBFh04eiYzjcK8cAB1sCGooio7OJvcKARg9mRtCCK1UkHVmGDRRiFiggBCoLVSQdUdnFmpk+gvgOXVNbmKz9wEgDwU8gqqxgTzUicc+gAgFAp5BVVjgmlplDzkxgGMozeFvM4sk0jVmGCZgVZx5MYBjKMXhTx6SFm3Jz1OTDAaaJW+TegF5MYBjKsXqZU2zDLJOwCCQx8A1DGzhTye985KykdjZqdRRA/u20WmHMBEzGQhLztiVio/ZrZu5psRswAmZSYLeZURs1J+myXUrPDo/RRuAKHN5MPOcWJ8Wd/T5DFuAFDGTBbyrBjfwvwwMwqY9T3MCgfQdjNZyPPy3ml/Zso+X5NZ4QDabiYLeV7eO7lJx6QLqZa0fDmzwgG0Xa0xtmZ2p6TflbSy+dL73P0fi76vLWNs9xw6kZrtXpgf6uTi3gtfh0itAEBdkxxje9jdPxTgOrVVLbh5/W+KN4CumJn44Tgxwazdli7pwNEzl7Rc8q4FAE0J0SO/zcweMrN7zGxb1pvM7FYzWzKzpZWVlay3jW2cmGDedMJkw4nIIYC2KizkZvYlM3sk5Z+bJX1U0ssl7Zb0tKQPZ13H3Y+4+8jdR9u3bw91/xeMExOsOp2QyCGANipsrbj7a8tcyMw+JukLte9oTFltkqKYYJRk2bl4PHMmS9lrAUATarVWzOxlsS/fKumRerczvroxwaIiTeQQQFvV7ZH/hZk9bGYPSXq1pAMB7mks48wKj8vaKKQxrgUA01QrteLu7wp1IyHUGUrFdEIAXTUz8cMQmE4IoIs6X8jZuAOg7zpdyEPOCgeArur00CxmhQNAxws5s8IBoEOtlbRe+LibgABglnRiRR71wpdX1+R6oRf+6l/azqxwAL3XiUKe1Qu/98En9dOXbdG2rYOxNgEBwCzoRGslr+e9urau4WBOh/fvpoAD6KVOrMiLet4kVQD0WScKed7c8AhJFQB91YnWSnwOSlpKRSKpAqC/OrEilzaK+cnFvbp7/26SKgAQ04kVeRxTCgHgYp0r5BJTCgEgrjOtFQBAOgo5AHQchRwAOo5CDgAdRyEHgI4zd5/+h5qtSPrO1D+4viskfb/pm5iivv28Ej9zX3T1Z/5Fd9+efLGRQt5VZrbk7qOm72Na+vbzSvzMfTFrPzOtFQDoOAo5AHQchbyaI03fwJT17eeV+Jn7YqZ+ZnrkANBxrMgBoOMo5ADQcRTyMZjZe83MzeyKpu9l0szsLjP7ppk9ZGafNbP5pu9pUszsJjN7zMweN7PFpu9n0szsajP7FzP7hpk9ambvafqepsHM5szstJl9oel7CYVCXpGZXS3pdZKebPpepuQBSa9091+V9F+S7mj4fibCzOYkfUTSGyRdK+ntZnZts3c1cc9J+gN3/2VJr5L0+z34mSXpPZK+0fRNhEQhr+6wpD+U1IunxO7+RXd/bvPLByVd1eT9TNANkh5392+7+08kfUrSzQ3f00S5+9Pu/rXN3/9QG8Vtpgf9m9lVkt4k6W+bvpeQKOQVmNlbJC27+9ebvpeG/Lakf2r6JiZkQdJ3Y18/pRkvanFmtkPS9ZL+o+FbmbS7tbEQe77h+wiqkycETZKZfUnSL6T80fslvU/S66d7R5OX9zO7++c23/N+bfyn+CemeW9TZCmv9eK/uszsRZI+I+l2d//fpu9nUszszZKecfdTZnZjw7cTFIU8wd1fm/a6mV0naaekr5uZtNFi+JqZ3eDu/zPFWwwu62eOmNm7Jb1Z0mt8djcePCXp6tjXV0k629C9TI2ZDbRRxD/h7vc1fT8TtkfSW8zsjZIul/RzZnavu7+z4fuqjQ1BYzKzJySN3L2LE9RKM7ObJP2lpN9095Wm72dSzOwybTzMfY2kZUlflfQOd3+00RubINtYkXxc0g/c/faGb2eqNlfk73X3Nzd8K0HQI0eRv5L0s5IeMLMzZvbXTd/QJGw+0L1N0v3aeOj36Vku4pv2SHqXpL2b/9+e2VytomNYkQNAx7EiB4COo5ADQMdRyAGg4yjkANBxFHIA6DgKOQB0HIUcADru/wEr3B9WRJllBwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = torch.linspace(-5, 5, 100)\n",
    "y = torch.sin(X * 8) + 2 * X + 4 + 0.2 * torch.rand_like(X)\n",
    "plt.scatter(X, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can clearly see a trend in the data. Let us use a combined kernel as follows:\n",
    "\n",
    "`Linear + RBF * Periodic`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyro.clear_param_store()\n",
    "linear = gp.kernels.Linear(\n",
    "    input_dim=1,\n",
    ")\n",
    "periodic = gp.kernels.Periodic(\n",
    "    input_dim=1, period=torch.tensor(0.5), lengthscale=torch.tensor(4.0)\n",
    ")\n",
    "rbf = gp.kernels.RBF(\n",
    "    input_dim=1, lengthscale=torch.tensor(0.5), variance=torch.tensor(0.5)\n",
    ")\n",
    "k1 = gp.kernels.Product(kern0=rbf, kern1=periodic)\n",
    "\n",
    "k = gp.kernels.Sum(linear, k1)\n",
    "model = gp.models.GPRegression(\n",
    "    X=X,\n",
    "    y=y,\n",
    "    kernel=k,\n",
    "    jitter=2e-3,\n",
    ")\n",
    "\n",
    "loss = gp.util.train(model)\n",
    "plot_loss(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, y, s=50, alpha=0.5)\n",
    "\n",
    "with torch.no_grad():\n",
    "    mean, var = model(X)\n",
    "_ = plt.plot(X, mean, color=\"C3\", lw=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that our combination of kernel does a fairly good job in learning the inherent trend and periodicity in the data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's all there is to it. For more details on the `pyro.contrib.gp` module see the [docs](http://docs.pyro.ai/en/dev/contrib/gp.html). For an example on binary classification see [here](https://prog-ml.github.io/notebooks/gaussian_processes/pyro-binary-classification.html), for an example on deep kernel learning see [here](https://prog-ml.github.io/notebooks/gaussian_processes/pyro-deep-gp.html), and for an advanced example for GP classification using deep kernel learning see [here](https://github.com/pyro-ppl/pyro/blob/dev/examples/contrib/gp/sv-dkl.py)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reference\n",
    "\n",
    "[1] `Deep Gaussian processes and variational propagation of uncertainty`,<br />&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "Andreas Damianou\n",
    "\n",
    "[2] `A unifying framework for sparse Gaussian process approximation using power expectation propagation`,<br />&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "Thang D. Bui, Josiah Yan, and Richard E. Turner\n",
    "\n",
    "[3] `Scalable variational Gaussian process classification`,<br />&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "James Hensman, Alexander G. de G. Matthews, and Zoubin Ghahramani\n",
    "\n",
    "[4] `Gaussian Processes for Machine Learning`,<br />&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "Carl E. Rasmussen, and Christopher K. I. Williams\n",
    "\n",
    "[5] `A Unifying View of Sparse Approximate Gaussian Process Regression`,<br />&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "Joaquin Quinonero-Candela, and Carl E. Rasmussen"
   ]
  }
 ],
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